Journal articles: 'Coset enumeration'

1

Linton, Stephen A. "Double coset enumeration." Journal of Symbolic Computation 12, no. 4-5 (October 1991): 415–26. http://dx.doi.org/10.1016/s0747-7171(08)80094-6.

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2

Sayed, Mohamed. "Coset enumeration of groups generated by symmetric sets of involutions." International Journal of Mathematics and Mathematical Sciences 2005, no. 23 (2005): 3739–50. http://dx.doi.org/10.1155/ijmms.2005.3739.

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All non-abelian finite simple groups can be symmetrically generated by involutions. An algorithm which performs coset enumeration for a group defined in this manner on the cosets of a subgroup of automorphisms of these involutions is presented.

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3

PIGGOTT, ADAM. "THE MANIFESTATION OF GROUP ENDS IN THE TODD–COXETER COSET ENUMERATION PROCEDURE." International Journal of Algebra and Computation 17, no. 01 (February 2007): 203–20. http://dx.doi.org/10.1142/s0218196707003561.

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The issue of recognizing group properties, such as the cardinality of the group, directly from the dynamics of an incomplete coset enumeration is discussed. In particular, it is shown that the property of having two ends is recognizable in such a way. Further, sufficient conditions are given for termination of a coset enumeration with the declaration that the group under consideration has infinitely-many ends.

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4

Reinert, Birgit, and Dirk Zeckzer. "Coset Enumeration Using Prefix Gröbner Bases: An Experimental Approach." LMS Journal of Computation and Mathematics 4 (2001): 74–134. http://dx.doi.org/10.1112/s1461157000000826.

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AbstractThe authors study a new method for coset enumeration in finitely presented groups. Their method uses prefix Gröbner basis computation in the monoid ring ${\mathbb{K}}[{\cal M}]$, where ${\mathbb{K}}$ is a computable field and ${\cal M}$ a monoid presented by a convergent string-rewriting system. The method is compared to well-known methods for Todd-Coxeter enumeration, using examples from the literature where studies of these methods are reported. New insights into coset enumeration were gained using three different kinds of orderings, combined with new frameworks and strategies implemented in MRC 1.2.

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Havas, George, and Colin Ramsay. "Proving a group trivial made easy: A case study in coset enumeration." Bulletin of the Australian Mathematical Society 62, no. 1 (August 2000): 105–18. http://dx.doi.org/10.1017/s0004972700018529.

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Coset enumeration, based on the methods described by Todd and Coxeter, is one of the basic tools for investigating finitely presented groups. The process is not well understood, and various pathological presentations of, for example, the trivial group have been suggested as challenge problems. Here we consider one such family of presentations proposed by B.H. Neumann. We show that the problems are much easier than they first appear, albeit at the expense of considerable preliminary ‘experimentation’. This demonstrates how far the range of applicability of coset enumeration has improved.

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6

HARTUNG, RENÉ. "COSET ENUMERATION FOR CERTAIN INFINITELY PRESENTED GROUPS." International Journal of Algebra and Computation 21, no. 08 (December 2011): 1369–80. http://dx.doi.org/10.1142/s0218196711006637.

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We describe an algorithm that computes the index of a finitely generated subgroup in a finitely L-presented group provided that this index is finite. This algorithm shows that the subgroup membership problem for finite index subgroups in a finitely L-presented group is decidable. As an application, we consider the low-index subgroups of some self-similar groups including the Grigorchuk group, the twisted twin of the Grigorchuk group, the Grigorchuk super-group, and the Hanoi 3-group.

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7

Sayed, Mohamed. "Double-coset enumeration algorithm for symmetrically generated groups." International Journal of Mathematics and Mathematical Sciences 2005, no. 5 (2005): 699–715. http://dx.doi.org/10.1155/ijmms.2005.699.

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8

Clark, Jeffrey W. "An APL implementation of Todd-Coxeter coset enumeration." ACM SIGAPL APL Quote Quad 21, no. 3 (March 1991): 7–11. http://dx.doi.org/10.1145/122442.122446.

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9

Akl, S., G. Labonté, M. Leeder, and K. Qiu. "On doing Todd-Coxeter coset enumeration in parallel." Discrete Applied Mathematics 34, no. 1-3 (November 1991): 27–35. http://dx.doi.org/10.1016/0166-218x(91)90076-9.

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10

Robertson, Edmund F., and Yusuf Ünlü. "On semigroup presentations." Proceedings of the Edinburgh Mathematical Society 36, no. 1 (February 1993): 55–68. http://dx.doi.org/10.1017/s0013091500005897.

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Semigroup presentations have been studied over a long period, usually as a means of providing examples of semigroups. In 1967 B. H. Neumann introduced an enumeration method for finitely presented semigroups analogous to the Todd–Coxeter coset enumeration process for groups. A proof of Neumann's enumeration method was given by Jura in 1978.In Section 3 of this paper we describe a machine implementation of a semigroup enumeration algorithm based on that of Neumann. In Section 2 we examine certain semigroup presentations, motivated by the fact that the corresponding group presentation has yielded interesting groups. The theorems, although proved algebraically, were suggested by the semigroup enumeration program.

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11

Sayed, Mohamed. "Combinatorial method in the coset enumeration of symmetrically generated groups." International Journal of Computer Mathematics 85, no. 7 (July 2008): 993–1001. http://dx.doi.org/10.1080/00207160701543376.

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12

Cooperman, Gene, and Victor Grinberg. "Scalable Parallel Coset Enumeration: Bulk Definition and the Memory Wall." Journal of Symbolic Computation 33, no. 5 (May 2002): 563–85. http://dx.doi.org/10.1006/jsco.2002.0523.

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13

Fujita, Shinsaku. "Sphericities of Double Cosets, Double Coset Representations, and Fujita’s Proligand Method for Combinatorial Enumeration of Stereoisomers." Journal of Mathematical Chemistry 42, no. 2 (May 17, 2006): 215–63. http://dx.doi.org/10.1007/s10910-006-9094-9.

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14

Sims, Charles C. "The Knuth-Bendix procedure for strings as a substitute for coset enumeration." Journal of Symbolic Computation 12, no. 4-5 (October 1991): 439–42. http://dx.doi.org/10.1016/s0747-7171(08)80096-x.

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15

Havas, George, Derek F. Holt, P. E. Kenne, and Sarah Rees. "Some challenging group presentations." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 67, no. 2 (October 1999): 206–13. http://dx.doi.org/10.1017/s1446788700001178.

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AbstractWe study some challenging presentations which arise as groups of deficiency zero. In four cases we settle finiteness: we show that two presentations are for finite groups while two are for infinite groups. Thus we answer three explicit questions in the literature and we provide the first published deficiency zero presentation for a group with derived length seven. The tools we use are coset enumeration and Knuth-Bebdix rewriting, which are well-established as methods for proving finiteness or otherwise of a finitely presented group. We briefly comment on their capabilities and compare their performance.

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16

Sayed, M. "Combinatorial method in the coset enumeration of symmetrically generated groups II: Monomial modular representations." International Journal of Algebra 1 (2007): 505–18. http://dx.doi.org/10.12988/ija.2007.07054.

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17

Fujita, Shinsaku. "Subduction of coset representations. An application to enumeration of chemical structures with achiral and chiral ligands." Journal of Mathematical Chemistry 5, no. 2 (June 1990): 121–56. http://dx.doi.org/10.1007/bf01166424.

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18

Campbell, Colin M., George Havas, Colin Ramsay, and Edmund F. Robertson. "Nice Efficient Presentions for all Small Simple Groups and their Covers." LMS Journal of Computation and Mathematics 7 (2004): 266–83. http://dx.doi.org/10.1112/s1461157000001121.

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AbstractPrior to this paper, all small simple groups were known to be efficient, but the status of four of their covering groups was unknown. Nice, efficient presentations are provided in this paper for all of these groups, resolving the previously unknown cases. The authors‘presentations are better than those that were previously available, in terms of both length and computational properties. In many cases, these presentations have minimal possible length. The results presented here are based on major amounts of computation. Substantial use is made of systems for computational group theory and, in partic-ular, of computer implementations of coset enumeration. To assist in reducing the number of relators, theorems are provided to enable the amalgamation of power relations in certain presentations. The paper concludes with a selection of unsolved problems about efficient presentations for simple groups and their covers.

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19

Fujita, Shinsaku. "Enumeration of organic reactions by counting substructures of imaginary transition structures. Importance of orbits governed by coset representations." Journal of Mathematical Chemistry 7, no. 1 (December 1991): 111–33. http://dx.doi.org/10.1007/bf01200819.

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20

Ellis, Graham, and Irina Kholodna. "Three-Dimensional Presentations for the Groups of Order at Most 30." LMS Journal of Computation and Mathematics 2 (1999): 93–117. http://dx.doi.org/10.1112/s1461157000000085.

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AbstractFor each group G of order up to 30 we compute a small 3-dimensional CW-space X with π1X≌ G and π2X = 0, and we quantify the ‘efficiency’ of X. Furthermore, we give a theoretical result for treating the case when G is a semi-direct product of two groups for which 3-presentations are known. We also describe the ZG-module structure on the second homotopy group π2X2 of the 2-skeleton of X. This module structure can in principle be used to determine the co-homology groups H2(G, A) and H3(G, A) with coefficients in a ZG-module A. Our computations, which involve the Todd–Coxeter procedure for coset enumeration and the LLL algorithm for finding bases of integer lattices, are rather naive in that the LLL algorithm is applied to matrices of dimension a multiple of |G|. Thus, in their present form, our techniques can be used only on small groups (say of order up to several hundred). They can in principle be used to construct (crossed) ZG-resolutions of Z, but again, only for small G. The paper is accompanied by two attachment files. The first of these is a summary of our computations in HTML format. The second contains various GAP programs used in the computations.

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21

Brocas, Jean. "Double cosets and enumeration of permutational isomers of fixed symmetry." Journal of the American Chemical Society 108, no. 6 (March 1986): 1135–45. http://dx.doi.org/10.1021/ja00266a004.

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22

McKnight, Alanna. "Dressmakers and Seamstresses in Toronto, 1834–1861." Costume 52, no. 1 (March 2018): 48–73. http://dx.doi.org/10.3366/cost.2018.0047.

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The young colonial city of Toronto was a landing place for many newcomers to Canada, and was a city of opportunity. The steady growth in population between 1834 and 1861 afforded women employment outside of the home, notably in the needle-trades (i.e. the roles involved in the manufacture of clothing). This article argues that the needle-trades were a significant source of employment for women in pre-industrial period Toronto and explores the social and professional distinctions between ‘dressmakers’ and ‘seamstresses’, by enumerating and aggregating women from the City Directories and 1861 census. Several biographical case studies are included to demonstrate the variety of women employed in the needle-trades, based on information from the primary source data.

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23

Kolarevic, S., Jelena Knezevic-Vukcevic, M. Paunovic, Jelena Tomovic, Z. Gacic, and Branka Vukovic-Gacic. "The anthropogenic impact on water quality of the river Danube in Serbia: Microbiological analysis and genotoxicity monitoring." Archives of Biological Sciences 63, no. 4 (2011): 1209–17. http://dx.doi.org/10.2298/abs1104209k.

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The aim of this work was to examine the impact of urban wastewaters on the water quality of the Danube River in Serbia. Samples of water and sediments for microbiological analysis and genotoxicity monitoring were collected from 6 sites during spring and/or autumn 2010. Sanitary analysis, i.e. enumeration of total and fecal coliforms and intestinal enterococci, indicated moderate to critical fecal contamination, while organic load assessment (oligotroph to heterotroph ratio, index of phosphatase activity) revealed the category of moderately polluted water. Mercury-resistant bacteria were detected in all water samples, with high numbers at locations positioned downstream of Belgrade. There was no correlation of the microbiological parameters of the sediment and water samples. Genotoxicity monitoring, performed by the comet assay on hemocytes of mussels Sinanodonta woodiana, indicated a significant increase of DNA damage in mussels collected from the studied sites compared with the control group.

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24

Müller, Jürgen, Max Neunhöffer, and Robert A. Wilson. "Enumerating big orbits and an application: B acting on the cosets of Fi23." Journal of Algebra 314, no. 1 (August 2007): 75–96. http://dx.doi.org/10.1016/j.jalgebra.2007.03.038.

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25

Fujita, Shinsaku. "Enumerations of chemical structures by subduction of coset representations. Correlation of unit subduced cycle indices to P�lya's cycle indices." Journal of Mathematical Chemistry 5, no. 2 (June 1990): 99–120. http://dx.doi.org/10.1007/bf01166423.

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26

Becker, Anja, Nicolas Gama, and Antoine Joux. "A sieve algorithm based on overlattices." LMS Journal of Computation and Mathematics 17, A (2014): 49–70. http://dx.doi.org/10.1112/s1461157014000229.

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AbstractIn this paper, we present a heuristic algorithm for solving exact, as well as approximate, shortest vector and closest vector problems on lattices. The algorithm can be seen as a modified sieving algorithm for which the vectors of the intermediate sets lie in overlattices or translated cosets of overlattices. The key idea is hence no longer to work with a single lattice but to move the problems around in a tower of related lattices. We initiate the algorithm by sampling very short vectors in an overlattice of the original lattice that admits a quasi-orthonormal basis and hence an efficient enumeration of vectors of bounded norm. Taking sums of vectors in the sample, we construct short vectors in the next lattice. Finally, we obtain solution vector(s) in the initial lattice as a sum of vectors of an overlattice. The complexity analysis relies on the Gaussian heuristic. This heuristic is backed by experiments in low and high dimensions that closely reflect these estimates when solving hard lattice problems in the average case.This new approach allows us to solve not only shortest vector problems, but also closest vector problems, in lattices of dimension$\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}n$in time$2^{0.3774\, n}$using memory$2^{0.2925\, n}$. Moreover, the algorithm is straightforward to parallelize on most computer architectures.

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27

Walter, Dagmar, Amelie Lier, Anja Geiselhart, Sina Huntscha, David Brocks, Irem Bayindir, Paul Kaschutnig, et al. "HSC Exit From Dormancy Provokes De Novo DNA Damage, Leading To Bone Marrow Failure If Unresolved By The Fanconi Anemia Pathway." Blood 122, no. 21 (November 15, 2013): 799. http://dx.doi.org/10.1182/blood.v122.21.799.799.

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Abstract Long-term quiescence has been proposed to preserve the genomic stability of hematopoietic stem cells (HSCs) during aging. The current models of HSC aging are limited in their ability to observe both DNA damage in vivo and the consequences of this damage upon hematopoiesis. Fanconi Anemia (FA) is a hereditary multisystem disorder, characterized by defective DNA damage response and progressive bone marrow failure in most patients. However, the existing genetic models of FA do not develop aplastic anemia, suggesting that cell-extrinsic factors may play a causal role. We sought to identify whether physiologic mediators of HSC activation could be used as agonists to provoke DNA damage and HSC attrition in vivo. Mice were treated with a range of agonists that promote the in vivo exit of HSC from a dormant state into active cycling (polyI:polyC; Interferon-α; G-CSF; TPO; and serial bleeding). Highly purified HSC demonstrated a rapid 3-5-fold induction of DNA damage after treatment with all agonists (p<0.01), as assessed by both enumerating γ-H2AX foci and by alkaline comet assay. Mechanistically, stress-induced exit from quiescence correlated with increased mitochondrial metabolism in HSC, as evaluated by elevated mitochondrial membrane potential (2-fold increased, p<0.01) and superoxide levels (1.5-fold increased, p<0.05). Critically, we could directly implicate these reactive oxygen species in DNA damage as we observed a 1.4-fold increase in 8-Oxo-dG lesions in HSC that had been activated into cycle in vivo(p<0.05). At 48 h post-treatment, γ-H2AX levels began to decrease and this repair was concomitant with an induction of the FA signaling pathway in HSC, as demonstrated by both increased levels of FA gene expression and elevated FANCD2 foci (4-fold induction, p<0.01). Treatment of Fanca-/- mice with polyI:polyC led to a HSC proliferative response comparable to wild type (WT) mice but resulted in a 2-fold higher level of activation-induced DNA damage (p<0.05), demonstrating that this repair pathway is involved in resolving activation-induced DNA damage. Four rounds of serial in vivo activation led to a permanent depletion of the most primitive label-retaining Fanca-/- HSC and this correlated with a 4-fold depletion of functional HSC (p<0.01) as defined by competitive repopulation assays. Subsequent rounds of HSC activation with polyI:polyC resulted in the onset of a severe aplastic anemia (SAA) in 33% of treated Fanca-/- mice but not in any of the WT controls. SSA was characterized by a dramatic reduction in bone marrow (BM) cellularity, profound thrombocytopenia (21-246x106 platelets/ml), leukocytopenia (0.4-0.5x106 WBC/ml), neutropenia (0.03-0.1x106/ml) and anemia (1.5-2.3 g/dL Hb). Examination of BM HSC/progenitors demonstrated nearly complete loss of HSC, MPP, CMP and CLP (depletion of ≥33x, 8x, 4x and 12x respectively compared to PBS-treated Fanca-/-controls). Taken together, these data demonstrates that enforced exit from dormancy in vivo leads to de novo DNA damage in HSC, which is repaired by activation of a FA-dependent DNA damage response. Furthermore, the highly penetrant bone marrow failure observed in Fanconi anemia patients can be recapitulated by the serial application of a physiologic HSC activating signal to Fanca-/- mice. This suggests that the BM failure in FA may be caused by an aberrant response to HSC activation, most likely during exposure to infection or other physiologic stressors. These data provides a novel link between pro-inflammatory cytokines, DNA damage and HSC dysfunction and may have important clinical implications relevant to both prevention of BM failure in FA and in the study of age-related hematopoietic defects in non-FA patients. Moreover, these data provide the first evidence that FA knockout mouse models accurately recapitulate and provide novel insights into the etiology of BM failure in patients with FA. Disclosures: No relevant conflicts of interest to declare.

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28

Bray, John N., and Robert T. Curtis. "Double coset enumeration of symmetrically generated groups." Journal of Group Theory 7, no. 2 (January 7, 2004). http://dx.doi.org/10.1515/jgth.2004.002.

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29

Exoo, Geoffrey. "Voltage Graphs, Group Presentations and Cages." Electronic Journal of Combinatorics 11, no. 1 (February 14, 2004). http://dx.doi.org/10.37236/1843.

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30

Diaconis, Persi, and Mackenzie Simper. "Statistical enumeration of groups by double cosets." Journal of Algebra, June 2021. http://dx.doi.org/10.1016/j.jalgebra.2021.05.010.

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31

CARTER, MAX, and GEORGE A. WILLIS. "DECOMPOSITION THEOREMS FOR AUTOMORPHISM GROUPS OF TREES." Bulletin of the Australian Mathematical Society, May 20, 2020, 1–9. http://dx.doi.org/10.1017/s0004972720000465.

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Motivated by the Bruhat and Cartan decompositions of general linear groups over local fields, we enumerate double cosets of the group of label-preserving automorphisms of a label-regular tree over the fixator of an end of the tree and over maximal compact open subgroups. This enumeration is used to show that every continuous homomorphism from the automorphism group of a label-regular tree has closed range.

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32

Vong, Vincent. "Algebraic properties for some permutation statistics." Discrete Mathematics & Theoretical Computer Science DMTCS Proceedings vol. AS,..., Proceedings (January 1, 2013). http://dx.doi.org/10.46298/dmtcs.2345.

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International audience In this article, we study some quotient sets on permutations built from peaks, valleys, double rises and double descents. One part is dedicated to the enumeration of the cosets using the bijection of Francon-Viennot which is a bijection between permutations and the so-called Laguerre histories. Then we study the algebraic properties of these quotient sets. After having shown that some of them give rise to quotient algebras of $\mathbf{FQSym}$, we prove that they are also free.

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33

BROCAS, J. "ChemInform Abstract: Double Cosets and Enumeration of Permutational Isomers of Fixed Symmetry." Chemischer Informationsdienst 17, no. 28 (July 15, 1986). http://dx.doi.org/10.1002/chin.198628039.

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34

Wu, Tingting, Shixin Zhu, Li Liu, and Lanqiang Li. "Repeated-root constacyclic codes of length 6l^mpⁿ." Advances in Mathematics of Communications, 2021, 0. http://dx.doi.org/10.3934/amc.2021044.

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<p style='text-indent:20px;'>Let <inline-formula><tex-math id="M1">\begin{document}$ \mathbb{F}_{q} $\end{document}</tex-math></inline-formula> be a finite field with character <inline-formula><tex-math id="M2">\begin{document}$ p $\end{document}</tex-math></inline-formula>. In this paper, the multiplicative group <inline-formula><tex-math id="M3">\begin{document}$ \mathbb{F}_{q}^{*} = \mathbb{F}_{q}\setminus\{0\} $\end{document}</tex-math></inline-formula> is decomposed into a mutually disjoint union of <inline-formula><tex-math id="M4">\begin{document}$ \gcd(6l^mp^n,q-1) $\end{document}</tex-math></inline-formula> cosets over subgroup <inline-formula><tex-math id="M5">\begin{document}$ <\xi^{6l^mp^n}> $\end{document}</tex-math></inline-formula>, where <inline-formula><tex-math id="M6">\begin{document}$ \xi $\end{document}</tex-math></inline-formula> is a primitive element of <inline-formula><tex-math id="M7">\begin{document}$ \mathbb{F}_{q} $\end{document}</tex-math></inline-formula>. Based on the decomposition, the structure of constacyclic codes of length <inline-formula><tex-math id="M8">\begin{document}$ 6l^mp^n $\end{document}</tex-math></inline-formula> over finite field <inline-formula><tex-math id="M9">\begin{document}$ \mathbb{F}_{q} $\end{document}</tex-math></inline-formula> and their duals is established in terms of their generator polynomials, where <inline-formula><tex-math id="M10">\begin{document}$ p\neq{3} $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M11">\begin{document}$ l\neq{3} $\end{document}</tex-math></inline-formula> are distinct odd primes, <inline-formula><tex-math id="M12">\begin{document}$ m $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M13">\begin{document}$ n $\end{document}</tex-math></inline-formula> are positive integers. In addition, we determine the characterization and enumeration of all linear complementary dual(LCD) negacyclic codes and self-dual constacyclic codes of length <inline-formula><tex-math id="M14">\begin{document}$ 6l^mp^n $\end{document}</tex-math></inline-formula> over <inline-formula><tex-math id="M15">\begin{document}$ \mathbb{F}_{q} $\end{document}</tex-math></inline-formula>.</p>

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Journal articles on the topic 'Coset enumeration'

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