Relevant bibliographies by topics / Cayley permutations

Academic literature on the topic 'Cayley permutations'

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Published: 10 March 2023

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Journal articles on the topic "Cayley permutations"

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CHITTURI, BHADRACHALAM. "UPPER BOUNDS FOR SORTING PERMUTATIONS WITH A TRANSPOSITION TREE." Discrete Mathematics, Algorithms and Applications 05, no. 01 (March 2013): 1350003. http://dx.doi.org/10.1142/s1793830913500031.

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An upper bound for sorting permutations with an operation estimates the diameter of the corresponding Cayley graph and an exact upper bound equals the diameter. Computing tight upper bounds for various operations is of theoretical and practical (e.g., interconnection networks, genetics) interest. Akers and Krishnamurthy gave a Ω(n! n2) time method that examines n! permutations to compute an upper bound, f(Γ), to sort any permutation with a given transposition tree T, where Γ is the Cayley graph corresponding to T. We compute two intuitive upper bounds γ and δ′ each in O(n2) time for the same, by working solely with the transposition tree. Recently, Ganesan computed β, an estimate of the exact upper bound for the same, in O(n2) time. Our upper bounds are tighter than f(Γ) and β, on average and in most of the cases. For a class of trees, we prove that the new upper bounds are tighter than β and f(Γ).
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Olshevskyi, M. S. "Metric properties of Cayley graphs of alternating groups." Carpathian Mathematical Publications 13, no. 2 (November 19, 2021): 545–81. http://dx.doi.org/10.15330/cmp.13.2.545-581.

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A well known diameter search problem for finite groups with respect to its systems of generators is considered. The problem can be formulated as follows: find the diameter of a group over its system of generators. The diameter of a group over a specific system of generators is the diameter of the corresponding Cayley graph. It is considered alternating groups with classic irreducible system of generators consisting of cycles with length three of the form $(1,2,k)$. The main part of the paper concentrates on analysis how even permutations decompose with respect to this system of generators. The rules for moving generators from permutation's decomposition from left to right and from right to left are introduced. These rules give rise for transformations of decompositions, that do not increase their lengths. They are applied for removing fixed points of a permutation, that were included in its decomposition. Based on this rule the stability of system of generators is proved. The strict growing property of the system of generators is also proved, as the corollary of transformation rules and the stability property. It is considered homogeneous theory, that was introduced in the previous author's paper. For the series of alternating groups with systems of generators mentioned above it is shown that this series is uniform and homogeneous. It makes possible to apply the homogeneous down search algorithm to compute the diameter. This algorithm is applied and exact values of diameters for alternating groups of degree up to 43 are computed.
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Olshevskyi, M. "The lower bound of diameter of Alternating groups." Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics, no. 4 (2021): 11–22. http://dx.doi.org/10.17721/1812-5409.2021/4.1.

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In this paper we consider a specific case of the diameter search problem for finite groups, thecase where the system of generators is fixed. This problem is well-known and can be formulated in the following way: find the diameter of a group over its system of generators. The diameter of the corresponding Cayley graph is the diameter of a group over its specific system of generators. The main object of the research is the alternating group with the system of generators consisting of cycles having length three and the form (1,2,k). This system of generators is a classical irreducible system of generators of the alternating group. It is introduced the property of even permutations to be balanced. We consider the set of balanced permutations and permutations close enough to balanced and find minimum decompositions of them over defined system of generators. The main result of the paper is the lower bound of the diameter of Alternating group over con-sidered system of generators. The estimation is achieved using minimal decompositions of balanced permutations.
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Babai, L., and G. L. Hetyei. "On the Diameter of Random Cayley Graphs of the Symmetric Group." Combinatorics, Probability and Computing 1, no. 3 (September 1992): 201–8. http://dx.doi.org/10.1017/s0963548300000237.

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Let σ, π be two permutations selected at random from the uniform distribution on the symmetric group Sn. By a result of Dixon [5], the subgroup G generated by σ, π is almost always (i.e. with probability approaching 1 as n → ∞) either Sn or the alternating group An. We prove that the diameter of the Cayley graph of G defined by {σ, π} is almost always not greater than exp ((½ + o(l)). (In n)2).
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Abdesselam, B., and A. Chakrabarti. "Multiparameter Statistical Models from Braid Matrices: Explicit Eigenvalues of Transfer Matrices , Spin Chains, Factorizable Scatterings for All." Advances in Mathematical Physics 2012 (2012): 1–21. http://dx.doi.org/10.1155/2012/193190.

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For a class of multiparameter statistical models based on braid matrices, the eigenvalues of the transfer matrix are obtained explicitly for all . Our formalism yields them as solutions of sets of linear equations with simple constant coefficients. The role of zero-sum multiplets constituted in terms of roots of unity is pointed out, and their origin is traced to circular permutations of the indices in the tensor products of basis states induced by our class of matrices. The role of free parameters, increasing as withN, is emphasized throughout. Spin chain Hamiltonians are constructed and studied for allN. Inverse Cayley transforms of the Yang-Baxter matrices corresponding to our braid matrices are obtained for allN. They provide potentials for factorizableS-matrices. Main results are summarized, and perspectives are indicated in the concluding remarks.
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Păun, Udrea. "$G$ method in action: Fast exact sampling from set of permutations of order $n$ according to Mallows model through Cayley metric." Brazilian Journal of Probability and Statistics 31, no. 2 (May 2017): 338–52. http://dx.doi.org/10.1214/16-bjps316.

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Skresanov, Saveliy V. "Subgroups of minimal index in polynomial time." Journal of Algebra and Its Applications 19, no. 01 (January 29, 2019): 2050010. http://dx.doi.org/10.1142/s0219498820500103.

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By applying an old result of Y. Berkovich, we provide a polynomial-time algorithm for computing the minimal possible index of a proper subgroup of a finite permutation group [Formula: see text]. Moreover, we find that subgroup explicitly and within the same time if [Formula: see text] is given by a Cayley table. As a corollary, we get an algorithm for testing whether or not a finite permutation group acts on a tree non-trivially.
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Alspach, Brian, and Shaofei Du. "Suborbit Structure of Permutation p-Groups and an Application to Cayley Digraph Isomorphism." Canadian Mathematical Bulletin 47, no. 2 (June 1, 2004): 161–67. http://dx.doi.org/10.4153/cmb-2004-017-9.

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AbstractLet P be a transitive permutation group of order pm, p an odd prime, containing a regular cyclic subgroup. The main result of this paper is a determination of the suborbits of P. The main result is used to give a simple proof of a recent result by J. Morris on Cayley digraph isomorphisms.
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LI, CAI HENG, and CHERYL E. PRAEGER. "SELF-COMPLEMENTARY VERTEX-TRANSITIVE GRAPHS NEED NOT BE CAYLEY GRAPHS." Bulletin of the London Mathematical Society 33, no. 6 (November 2001): 653–61. http://dx.doi.org/10.1112/s0024609301008505.

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A construction is given of an infinite family of finite self-complementary, vertex-transitive graphs which are not Cayley graphs. To the authors' knowledge, these are the first known examples of such graphs. The nature of the construction was suggested by a general study of the structure of self-complementary, vertex-transitive graphs. It involves the product action of a wreath product of permutation groups.
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Kuznetsov, А. A., and V. V. Kishkan. "A ROUTING ALGORITHM FOR THE CAYLEY GRAPHS GENERATED BY PERMUTATION GROUPS." Siberian Journal of Science and Technology 21, no. 2 (2020): 187–94. http://dx.doi.org/10.31772/2587-6066-2020-21-2-187-194.

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Dissertations / Theses on the topic "Cayley permutations"

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Muthivhi, Thifhelimbilu Ronald. "Codes Related to and Derived from Hamming Graphs." University of the Western Cape, 2013. http://hdl.handle.net/11394/4091.

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Masters of Science
Codes Related to and Derived from Hamming Graphs T.R Muthivhi M.Sc thesis, Department of Mathematics, University of Western Cape For integers n; k 1; and k n; the graph 􀀀k n has vertices the 2n vectors of Fn2 and adjacency de ned by two vectors being adjacent if they di er in k coordinate positions. In particular, 􀀀1 n is the classical n-cube, usually denoted by H1(n; 2): This study examines the codes (both binary and p-ary for p an odd prime) of the row span of adjacency and incidence matrices of these graphs. We rst examine codes of the adjacency matrices of the n-cube. These have been considered in [14]. We then consider codes generated by both incidence and adjacency matrices of the Hamming graphs H1(n; 3) [12]. We will also consider codes of the line graphs of the n-cube as in [13]. Further, the automorphism groups of the codes, designs and graphs will be examined, highlighting where there is an interplay. Where possible, suitable permutation decoding sets will be given.
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Cerbai, Giulio. "Sorting permutations with pattern-avoiding machines." Doctoral thesis, 2021. http://hdl.handle.net/2158/1235854.

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In this work of thesis we introduce and study a new family of sorting devices, which we call pattern-avoiding machines. They consist of two stacks in series, equipped with a greedy procedure. On both stacks we impose a static constraint in terms of pattern containment: reading the content from top to bottom, the first stack is not allowed to contain occurrences of a given pattern, whereas the second one is not allowed to contain occurrences of 21. By analyzing the behavior of pattern-avoding machines, we aim to gain a better understanding of the problem of sorting permutations with two consecutive stacks, which is currently one of the most challenging open problems in combinatorics.
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Book chapters on the topic "Cayley permutations"

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Grammatikakis, Miltos D., and Jung-Sing Jwo. "Greedy permutation routing on Cayley graphs." In Parallel Processing: CONPAR 92—VAPP V, 839–40. Berlin, Heidelberg: Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/3-540-55895-0_515.

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Cooperman, Gene, and Larry Finkelstein. "Permutation routing via Cayley graphs with an example for bus interconnection networks." In DIMACS Series in Discrete Mathematics and Theoretical Computer Science, 47–56. Providence, Rhode Island: American Mathematical Society, 1995. http://dx.doi.org/10.1090/dimacs/021/05.

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Hook, Julian. "Groups II." In Exploring Musical Spaces, 209–51. Oxford University PressNew York, 2023. http://dx.doi.org/10.1093/oso/9780190246013.003.0006.

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Abstract This chapter opens Part Two, devoted to the study of transformation theory, with some additional topics in group theory that arise in musical applications. Transformation groups on finite spaces may be regarded as permutation groups; permutation groups on pitch-class space include not only the groups of transpositions and inversions but also the multiplication group, the affine group, and the symmetric group. Another musical illustration of permutations involves the rearrangement of lines in invertible counterpoint. The structure of a finite group may be represented in the form of a group table or a Cayley diagram (a kind of graph). Other concepts discussed include homomorphisms and isomorphisms of groups, direct-product groups, normal subgroups, and quotient groups. Groups underlie many examples of symmetry in music, as formalized through the study of equivalence relations, orbits, and stabilizers.
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"Cayley graph and defining relations." In Fundamental Algorithms for Permutation Groups, 33–43. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/3-540-54955-2_24.

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Conference papers on the topic "Cayley permutations"

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PRAEGER, CHERYL E. "REGULAR PERMUTATION GROUPS AND CAYLEY GRAPHS." In Proceedings of the 13th General Meeting. WORLD SCIENTIFIC, 2009. http://dx.doi.org/10.1142/9789814277686_0003.

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Yang, Siyi, Clayton Schoeny, and Lara Dolecek. "Order-optimal permutation codes in the generalized cayley metric." In 2017 IEEE Information Theory Workshop (ITW). IEEE, 2017. http://dx.doi.org/10.1109/itw.2017.8277943.

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de Lima, Thaynara Arielly, and Mauricio Ayala-Rincon. "Complexity of Cayley distance and other general metrics on permutation groups." In 2012 7th Colombian Computing Congress (CCC). IEEE, 2012. http://dx.doi.org/10.1109/colombiancc.2012.6398020.

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Chee, Yeow Meng, and Van Khu Vu. "Breakpoint analysis and permutation codes in generalized Kendall tau and Cayley metrics." In 2014 IEEE International Symposium on Information Theory (ISIT). IEEE, 2014. http://dx.doi.org/10.1109/isit.2014.6875376.

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Yeh, C. H., and B. Parhami. "Parallel algorithms for index-permutation graphs. An extension of Cayley graphs for multiple chip-multiprocessors (MCMP)." In Proceedings International Conference on Parallel Processing. IEEE, 2001. http://dx.doi.org/10.1109/icpp.2001.952041.

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