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Journal articles on the topic 'Combinatorics of cores'

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Published: 5 October 2024

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1

Aukerman, David, Ben Kane, and Lawrence Sze. "On simultaneous s-cores/t-cores." Discrete Mathematics 309, no. 9 (May 2009): 2712–20. http://dx.doi.org/10.1016/j.disc.2008.06.024.

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2

Godsil, Chris, and Gordon F. Royle. "Cores of Geometric Graphs." Annals of Combinatorics 15, no. 2 (May 15, 2011): 267–76. http://dx.doi.org/10.1007/s00026-011-0094-5.

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3

Mančinska, Laura, Irene Pivotto, David E. Roberson, and Gordon F. Royle. "Cores of cubelike graphs." European Journal of Combinatorics 87 (June 2020): 103092. http://dx.doi.org/10.1016/j.ejc.2020.103092.

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4

Han, Guo-Niu, and Ken Ono. "Hook Lengths and 3-Cores." Annals of Combinatorics 15, no. 2 (May 15, 2011): 305–12. http://dx.doi.org/10.1007/s00026-011-0096-3.

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5

Sato, Cristiane M. "On the robustness of randomk-cores." European Journal of Combinatorics 41 (October 2014): 163–82. http://dx.doi.org/10.1016/j.ejc.2014.03.007.

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6

Malen, Greg. "Homomorphism complexes andk-cores." Discrete Mathematics 341, no. 9 (September 2018): 2567–74. http://dx.doi.org/10.1016/j.disc.2018.06.014.

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7

Cho, Hyunsoo, and Kyounghwan Hong. "Corners of self-conjugate (s,s + 1)-cores and (s‾,s+1‾)-cores." Discrete Mathematics 345, no. 9 (September 2022): 112949. http://dx.doi.org/10.1016/j.disc.2022.112949.

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8

Baruah, Nayandeep Deka, and Kallol Nath. "Infinite families of arithmetic identities for self-conjugate 5-cores and 7-cores." Discrete Mathematics 321 (April 2014): 57–67. http://dx.doi.org/10.1016/j.disc.2013.12.019.

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9

Thiel, Marko, and Nathan Williams. "Strange expectations and simultaneous cores." Journal of Algebraic Combinatorics 46, no. 1 (April 10, 2017): 219–61. http://dx.doi.org/10.1007/s10801-017-0754-6.

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10

Kotsireas, Ilias S., Christos Koukouvinos, and Jennifer Seberry. "Hadamard ideals and Hadamard matrices with two circulant cores." European Journal of Combinatorics 27, no. 5 (July 2006): 658–68. http://dx.doi.org/10.1016/j.ejc.2005.03.004.

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11

Haglund, Jim, Ken Ono, and Lawrence Sze. "Rook Theory andt-Cores." Journal of Combinatorial Theory, Series A 84, no. 1 (October 1998): 9–37. http://dx.doi.org/10.1006/jcta.1998.2874.

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12

Marietti, Mario, and Damiano Testa. "Cores of Simplicial Complexes." Discrete & Computational Geometry 40, no. 3 (May 15, 2008): 444–68. http://dx.doi.org/10.1007/s00454-008-9081-y.

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13

Paramonov, Kirill. "Cores with distinct parts and bigraded Fibonacci numbers." Discrete Mathematics 341, no. 4 (April 2018): 875–88. http://dx.doi.org/10.1016/j.disc.2017.12.010.

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14

Boros, E., and V. Gurvich. "Perfect graphs, kernels, and cores of cooperative games." Discrete Mathematics 306, no. 19-20 (October 2006): 2336–54. http://dx.doi.org/10.1016/j.disc.2005.12.031.

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15

Solymosi, David, and Jozsef Solymosi. "Small cores in 3-uniform hypergraphs." Journal of Combinatorial Theory, Series B 122 (January 2017): 897–910. http://dx.doi.org/10.1016/j.jctb.2016.11.001.

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16

Bowditch, Brian. "An upper bound for injectivity radii in convex cores." Groups, Geometry, and Dynamics 7, no. 1 (2013): 109–26. http://dx.doi.org/10.4171/ggd/178.

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17

Berkovich, Alexander, and Hamza Yesilyurt. "New identities for 7-cores with prescribed BG-rank." Discrete Mathematics 308, no. 22 (November 2008): 5246–59. http://dx.doi.org/10.1016/j.disc.2007.09.044.

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18

Butkovič, Peter, Hans Schneider, Sergeĭ Sergeev, and Bit-Shun Tam. "Two cores of a nonnegative matrix." Linear Algebra and its Applications 439, no. 7 (October 2013): 1929–54. http://dx.doi.org/10.1016/j.laa.2013.05.029.

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19

Ono, Ken, and Wissam Raji. "Class numbers and self-conjugate 7-cores." Journal of Combinatorial Theory, Series A 180 (May 2021): 105427. http://dx.doi.org/10.1016/j.jcta.2021.105427.

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20

Olsson, Jørn B. "A theorem on the cores of partitions." Journal of Combinatorial Theory, Series A 116, no. 3 (April 2009): 733–40. http://dx.doi.org/10.1016/j.jcta.2008.08.004.

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21

Bauslaugh, Bruce L. "Cores and Compactness of Infinite Directed Graphs." Journal of Combinatorial Theory, Series B 68, no. 2 (November 1996): 255–76. http://dx.doi.org/10.1006/jctb.1996.0068.

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22

Liu, Juan, Hong Yang, Xindong Zhang, and Hong-Jian Lai. "Symmetric cores and extremal size bound for supereulerian semicomplete bipartite digraphs." Discrete Mathematics 347, no. 4 (April 2024): 113867. http://dx.doi.org/10.1016/j.disc.2023.113867.

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23

Anderson, Jaclyn. "On the existence of rook equivalent t-cores." Journal of Combinatorial Theory, Series A 106, no. 2 (May 2004): 221–36. http://dx.doi.org/10.1016/j.jcta.2004.01.010.

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24

Lulov, Nathan, and Boris Pittel. "On the Random Young Diagrams and Their Cores." Journal of Combinatorial Theory, Series A 86, no. 2 (May 1999): 245–80. http://dx.doi.org/10.1006/jcta.1998.2939.

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25

Osoba, Benard, and Temitope Gbolahan Jaiyeola. "Algebraic connections between right and middle Bol loops and their cores." Quasigroups and Related Systems 30, no. 1(47) (May 2022): 149–60. http://dx.doi.org/10.56415/qrs.v30.13.

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To every right or left Bol loop corresponds a middle Bol loop. In this paper, the cores of right Bol loops (RBL) and its corresponding middle Bol loops (MBL) were studied. Their algebraic connections were considered. It was shown that the core of a RBL is elastic and right idempotent. The core of a RBL was found to be alternative (or left idempotent) if and only if its corresponding MBL is right symmetric. If a MBL is right (left) symmetric, then, the core of its corresponding RBL is a medial (semimedial). The core of a middle Bol loop has the left inverse property (automorphic inverse property, right idempotence resp.) if and only if its corresponding RBL has the super anti-automorphic inverse property (automorphic inverse property, exponent 2 resp.). If a RBL is of exponent 2, then, the core of its corresponding MBL is left idempotent. If a RBL is of exponent 2 then: the core of a MBL has the left alternative property (right alternative property) if and only if its corresponding RBL has the cross inverse property (middle symmetry). Some other similar results were derived for RBL of exponent 3.
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26

Tarau, Paul. "Deriving Efficient Sequential and Parallel Generators for Closed Simply-Typed Lambda Terms and Normal Forms." Fundamenta Informaticae 177, no. 3-4 (December 10, 2020): 385–415. http://dx.doi.org/10.3233/fi-2020-1994.

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Contrary to several other families of lambda terms, no closed formula or generating function is known and none of the sophisticated techniques devised in analytic combinatorics can currently help with counting or generating the set of simply-typed closed lambda terms of a given size. Moreover, their asymptotic scarcity among the set of closed lambda terms makes counting them via brute force generation and type inference quickly intractable, with previous published work showing counts for them only up to size 10. By taking advantage of the synergy between logic variables, unification with occurs check and efficient backtracking in today’s Prolog systems, we climb 4 orders of magnitude above previously known counts by deriving progressively faster sequential Prolog programs that generate and/or count the set of closed simply-typed lambda terms of sizes up to 14. Similar counts for closed simply-typed normal forms are also derived up to size 14. Finally, we devise several parallel execution algorithms, based on generating code to be uniformly distributed among the available cores, that push the counts for simply typed terms up to size 15 and simply typed normal forms up to size 16. As a remarkable feature, our parallel algorithms are linearly scalable with the number of available cores.
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27

Bonato, Anthony, and Paweł Prałat. "The good, the bad, and the great: Homomorphisms and cores of random graphs." Discrete Mathematics 309, no. 18 (September 2009): 5535–39. http://dx.doi.org/10.1016/j.disc.2008.03.026.

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28

Cho, Hyunsoo, JiSun Huh, Hayan Nam, and Jaebum Sohn. "Results on bar-core partitions, core shifted Young diagrams, and doubled distinct cores." Discrete Mathematics 346, no. 7 (July 2023): 113387. http://dx.doi.org/10.1016/j.disc.2023.113387.

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29

DeBiasio, Louis, András Gyárfás, and Gábor N. Sárközy. "Ramsey numbers of path-matchings, covering designs, and 1-cores." Journal of Combinatorial Theory, Series B 146 (January 2021): 124–40. http://dx.doi.org/10.1016/j.jctb.2020.09.004.

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30

González-Torres, Raúl E. "A geometric study of cores of idempotent stochastic matrices." Linear Algebra and its Applications 527 (August 2017): 87–127. http://dx.doi.org/10.1016/j.laa.2017.03.032.

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31

Mardiningsih, Saib Suwilo, and Ihda Hasbiyati. "Existence of Polynomial Combinatorics Graph Solution." Journal of Research in Mathematics Trends and Technology 2, no. 1 (February 24, 2020): 7–13. http://dx.doi.org/10.32734/jormtt.v2i1.3755.

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The Polynomial Combinatorics comes from optimization problem combinatorial in form the nonlinear and integer programming. This paper present a condition such that the polynomial combinatorics has solution. Existence of optimum value will be found by restriction of decision variable and properties of feasible solution set or polyhedra.
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32

Damaschke, Peter. "Multiple hypernode hitting sets and smallest two-cores with targets." Journal of Combinatorial Optimization 18, no. 3 (May 29, 2009): 294–306. http://dx.doi.org/10.1007/s10878-009-9234-9.

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33

Lapointe, Luc, and Jennifer Morse. "Tableaux on k+1-cores, reduced words for affine permutations, and k-Schur expansions." Journal of Combinatorial Theory, Series A 112, no. 1 (October 2005): 44–81. http://dx.doi.org/10.1016/j.jcta.2005.01.003.

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34

Giusti, Chad, and Vladimir Itskov. "A No-Go Theorem for One-Layer Feedforward Networks." Neural Computation 26, no. 11 (November 2014): 2527–40. http://dx.doi.org/10.1162/neco_a_00657.

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It is often hypothesized that a crucial role for recurrent connections in the brain is to constrain the set of possible response patterns, thereby shaping the neural code. This implies the existence of neural codes that cannot arise solely from feedforward processing. We set out to find such codes in the context of one-layer feedforward networks and identified a large class of combinatorial codes that indeed cannot be shaped by the feedforward architecture alone. However, these codes are difficult to distinguish from codes that share the same sets of maximal activity patterns in the presence of subtractive noise. When we coarsened the notion of combinatorial neural code to keep track of only maximal patterns, we found the surprising result that all such codes can in fact be realized by one-layer feedforward networks. This suggests that recurrent or many-layer feedforward architectures are not necessary for shaping the (coarse) combinatorial features of neural codes. In particular, it is not possible to infer a computational role for recurrent connections from the combinatorics of neural response patterns alone. Our proofs use mathematical tools from classical combinatorial topology, such as the nerve lemma and the existence of an inverse nerve. An unexpected corollary of our main result is that any prescribed (finite) homotopy type can be realized by a subset of the form [Formula: see text], where [Formula: see text] is a polyhedron.
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35

Da Rocha, V. C. "Combinatorial codes." Electronics Letters 21, no. 21 (1985): 949. http://dx.doi.org/10.1049/el:19850670.

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36

Wallace, Mark, and Neil Yorke-Smith. "A new constraint programming model and solving for the cyclic hoist scheduling problem." Constraints 25, no. 3-4 (November 9, 2020): 319–37. http://dx.doi.org/10.1007/s10601-020-09316-z.

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AbstractThe cyclic hoist scheduling problem (CHSP) is a well-studied optimisation problem due to its importance in industry. Despite the wide range of solving techniques applied to the CHSP and its variants, the models have remained complicated and inflexible, or have failed to scale up with larger problem instances. This article re-examines modelling of the CHSP and proposes a new simple, flexible constraint programming formulation. We compare current state-of-the-art solving technologies on this formulation, and show that modelling in a high-level constraint language, MiniZinc, leads to both a simple, generic model and to computational results that outperform the state of the art. We further demonstrate that combining integer programming and lazy clause generation, using the multiple cores of modern processors, has potential to improve over either solving approach alone.
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37

HIRD, J. T., NAIHUAN JING, and ERNEST STITZINGER. "CODES AND SHIFTED CODES." International Journal of Algebra and Computation 22, no. 06 (August 31, 2012): 1250054. http://dx.doi.org/10.1142/s0218196712500543.

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The action of the Bernstein operators on Schur functions was given in terms of codes by Carrell and Goulden (2011) and extended to the analog in Schur Q-functions in our previous work. We define a new combinatorial model of extended codes and show that both of these results follow from a natural combinatorial relation induced on codes. The new algebraic structure provides a natural setting for Schur functions indexed by compositions.
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38

B. Paterson, M., D. R. Stinson, and R. Wei. "Combinatorial batch codes." Advances in Mathematics of Communications 3, no. 1 (2009): 13–27. http://dx.doi.org/10.3934/amc.2009.3.13.

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39

Davidson, Ruth, and Seth Sullivant. "Polyhedral combinatorics of UPGMA cones." Advances in Applied Mathematics 50, no. 2 (February 2013): 327–38. http://dx.doi.org/10.1016/j.aam.2012.10.002.

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40

Krieger, M. H. "Where Do Centers Come From?" Environment and Planning A: Economy and Space 19, no. 9 (September 1987): 1251–60. http://dx.doi.org/10.1068/a191251.

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A ‘center’ is a marked place in space or time or in a collection of objects, and surrounding it is a structure or pattern that supports it. The questions that concern us here are: ‘Why are there centers at all?’ ‘Why is a center at a particular X?’ Historical and combinatorial processes of centralization are reviewed, and a phenomenology and mechanisms are provided. Models considered include: stochastic markets with increasing returns to scale, codes as in DNA, combinatoric processes as in statistical mechanics, and differentiation in biology. Polycenters.
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41

HIRD, J. T., NAIHUAN JING, and ERNEST STITZINGER. "CODES AND SHIFTED CODES OF PARTITIONS." International Journal of Algebra and Computation 21, no. 08 (December 2011): 1447–62. http://dx.doi.org/10.1142/s0218196711006595.

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In a recent paper, Carrell and Goulden found a combinatorial identity of the Bernstein operators that they then used to prove Bernstein's theorem. We show that this identity is a straightforward consequence of the classical result. We also show how a similar approach using the codes of partitions can be generalized from Schur functions to also include Schur Q-functions and derive the combinatorial formulation for both cases. We then apply them by examining the Littlewood–Richardson and Pieri rules.
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42

García-Calcines, José Manuel, Luis Javier Hernández-Paricio, and María Teresa Rivas-Rodríguez. "Augmented Simplicial Combinatorics through Category Theory: Cones, Suspensions and Joins." Mathematics 10, no. 4 (February 14, 2022): 590. http://dx.doi.org/10.3390/math10040590.

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In this work, we analyze the combinatorial properties of the category of augmented semi-simplicial sets. We consider various monoidal structures induced by the co-product, the product, and the join operator in this category. In addition, we also consider monoidal structures on augmented sequences of integers induced by the sum and product of integers and by the join of augmented sequences. The cardinal functor that associates to each finite set X its cardinal |X| induces the sequential cardinal that associates to each augmented semi-simplicial finite set X an augmented sequence |X|n of non-negative integers. We prove that the sequential cardinal functor is monoidal for the corresponding monoidal structures. This allows us to easily calculate the number of simplices of cones and suspensions of an augmented semi-simplicial set as well as other augmented semi-simplicial sets which are built by joins. In this way, the monoidal structures of the augmented sequences of numbers may be thought of as an algebraization of the augmented semi-simplicial sets that allows us to do a simpler study of the combinatorics of the augmented semi-simplicial finite sets.
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43

Aggarwal, Divesh, Yevgeniy Dodis, and Shachar Lovett. "Non-Malleable Codes from Additive Combinatorics." SIAM Journal on Computing 47, no. 2 (January 2018): 524–46. http://dx.doi.org/10.1137/140985251.

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44

Ghazi, Arjumand, and K. VijayRaghavan. "Control by combinatorial codes." Nature 408, no. 6811 (November 2000): 419–20. http://dx.doi.org/10.1038/35044174.

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45

Zhang, Hui, Eitan Yaakobi, and Natalia Silberstein. "Multiset combinatorial batch codes." Designs, Codes and Cryptography 86, no. 11 (February 23, 2018): 2645–60. http://dx.doi.org/10.1007/s10623-018-0468-3.

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46

HSIEH, CHUN-CHUNG. "COMBINATORIC MASSEY–MILNOR LINKING THEORY." Journal of Knot Theory and Its Ramifications 20, no. 06 (June 2011): 927–38. http://dx.doi.org/10.1142/s0218216511009030.

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In this paper following the scheme of Massey–Milnor invariant theory [C. C. Hsieh, Combinatoric and diagrammatic studies in knot theory J. Knot Theory Ramifications16 (2007) 1235–1253; C. C. Hsieh, Massey-Milnor linking = Chern-Simons-Witten graphs, J. Knot Theory Ramifications17 (2008) 877–903; C. C. Hsieh and S. W. Yang, Chern-Simons-Witten configuration space integrals in knot theory, J. Knot Theory Ramifications14 (2005) 689–711], we studied the first non-vanishing linkings of knot theory in ℝ3 and also derived the combinatorial formulae from which we could read out the invariants directly from the knot diagrams. Though the theme is calculus, the idea comes from perturbative quantum field theory.
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47

Sneyd, Alison. "Codes over rings and applications to combinatorics." Irish Mathematical Society Bulletin 0072 (2013): 37. http://dx.doi.org/10.33232/bims.0072.37.

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48

Ghorpade, Sudhir R., and Michael A. Tsfasman. "Schubert varieties, linear codes and enumerative combinatorics." Finite Fields and Their Applications 11, no. 4 (November 2005): 684–99. http://dx.doi.org/10.1016/j.ffa.2004.09.002.

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49

Stinson, D. R. "The combinatorics of authentication and secrecy codes." Journal of Cryptology 2, no. 1 (February 1990): 23–49. http://dx.doi.org/10.1007/bf02252868.

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50

Alami, Mustapha, Mohamed Bekkali, Latifa Faouzi, and Driss Zhani. "Free poset algebras and combinatorics of cones." Annals of Mathematics and Artificial Intelligence 49, no. 1-4 (June 13, 2007): 15–26. http://dx.doi.org/10.1007/s10472-007-9058-1.

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