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Journal articles on the topic 'Multipermutations'

Author: Grafiati

Published: 4 June 2021

Last updated: 15 February 2022

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1

Park, SeungKyung. "The r-multipermutations." Journal of Combinatorial Theory, Series A 67, no. 1 (July 1994): 44–71. http://dx.doi.org/10.1016/0097-3165(94)90003-5.

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2

Dzhumadil’daev, A. S. "Worpitzky identity for multipermutations." Mathematical Notes 90, no. 3-4 (September 2011): 448–50. http://dx.doi.org/10.1134/s0001434611090136.

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3

Park, SeungKyung. "Inverse descents of r-multipermutations." Discrete Mathematics 132, no. 1-3 (September 1994): 215–29. http://dx.doi.org/10.1016/0012-365x(94)90239-9.

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4

Lin, Zhicong. "On the descent polynomial of signed multipermutations." Proceedings of the American Mathematical Society 143, no. 9 (March 18, 2015): 3671–85. http://dx.doi.org/10.1090/s0002-9939-2015-12555-5.

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5

Lin, Zhicong, Jun Ma, and Philip B. Zhang. "Statistics on multipermutations and partial γ-positivity." Journal of Combinatorial Theory, Series A 183 (October 2021): 105488. http://dx.doi.org/10.1016/j.jcta.2021.105488.

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6

Rawlings, Don. "Bernoulli trials and permutation statistics." International Journal of Mathematics and Mathematical Sciences 15, no. 2 (1992): 291–311. http://dx.doi.org/10.1155/s0161171292000371.

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Several coin-tossing games are surveyed which, in a natural way, give rise to statistically induced probability measures on the set of permutations of{1,2,…,n}and on sets of multipermutations. The distributions of a general class of random variables known as binary tree statistics are also given.

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7

Chee, Yeow Meng, San Ling, Tuan Thanh Nguyen, Van Khu Vu, Hengjia Wei, and Xiande Zhang. "Burst-Deletion-Correcting Codes for Permutations and Multipermutations." IEEE Transactions on Information Theory 66, no. 2 (February 2020): 957–69. http://dx.doi.org/10.1109/tit.2019.2933819.

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8

Liu, Xishuo, and Stark C. Draper. "LP-Decodable Multipermutation Codes." IEEE Transactions on Information Theory 62, no. 4 (April 2016): 1631–48. http://dx.doi.org/10.1109/tit.2016.2526655.

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9

ZHAO, Peng, Jianjun MU, Yucheng HE, and Xiaopeng JIAO. "Multipermutation Codes Correcting a Burst of Deletions." IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E101.A, no. 2 (2018): 535–38. http://dx.doi.org/10.1587/transfun.e101.a.535.

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10

Yang, Z. F. "Multipermutation-Based Intersection Theorem and Its Applications." Journal of Optimization Theory and Applications 104, no. 2 (February 2000): 477–87. http://dx.doi.org/10.1023/a:1004626216810.

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11

Gionfriddo, Mario, Filippo Milazzo, and Vincenzo Vacirca. "Transitive multipermutation graphs: Case 4 ⩽ n ⩽ m." Discrete Mathematics 97, no. 1-3 (December 1991): 191–98. http://dx.doi.org/10.1016/0012-365x(91)90434-4.

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12

Gateva-Ivanova, Tatiana, and Peter Cameron. "Multipermutation Solutions of the Yang–Baxter Equation." Communications in Mathematical Physics 309, no. 3 (December 13, 2011): 583–621. http://dx.doi.org/10.1007/s00220-011-1394-7.

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13

Jedlička, Přemysl, Agata Pilitowska, and Anna Zamojska-Dzienio. "Distributive biracks and solutions of the Yang–Baxter equation." International Journal of Algebra and Computation 30, no. 03 (January 21, 2020): 667–83. http://dx.doi.org/10.1142/s0218196720500150.

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We investigate a class of non-involutive solutions of the Yang–Baxter equation which generalize derived (self-distributive) solutions. In particular, we study generalized multipermutation solutions in this class. We show that the Yang–Baxter (permutation) groups of such solutions are nilpotent. We formulate the results in the language of biracks which allows us to apply universal algebra tools.

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14

Burstein, Alexander, and Toufik Mansour. "Words Restricted by 3-Letter Generalized Multipermutation Patterns." Annals of Combinatorics 7, no. 1 (June 2003): 1–14. http://dx.doi.org/10.1007/s000260300000.

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15

ZHAO, Peng, Jianjun MU, and Xiaopeng JIAO. "Multipermutation Codes Correcting a Predetermined Number of Adjacent Deletions." IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E100.A, no. 10 (2017): 2176–79. http://dx.doi.org/10.1587/transfun.e100.a.2176.

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16

Gateva-Ivanova, Tatiana, and Shahn Majid. "Quantum Spaces Associated to Multipermutation Solutions of Level Two." Algebras and Representation Theory 14, no. 2 (December 24, 2009): 341–76. http://dx.doi.org/10.1007/s10468-009-9192-z.

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17

Farnoud Hassanzadeh, Farzad, and Olgica Milenkovic. "Multipermutation Codes in the Ulam Metric for Nonvolatile Memories." IEEE Journal on Selected Areas in Communications 32, no. 5 (May 2014): 919–32. http://dx.doi.org/10.1109/jsac.2014.140512.

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18

Jedlička, Přemysl, Agata Pilitowska, and Anna Zamojska-Dzienio. "Indecomposable involutive solutions of the Yang–Baxter equation of multipermutational level 2 with abelian permutation group." Forum Mathematicum 33, no. 5 (August 26, 2021): 1083–96. http://dx.doi.org/10.1515/forum-2021-0130.

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Abstract We present a construction of all finite indecomposable involutive solutions of the Yang–Baxter equation of multipermutational level at most 2 with abelian permutation group. As a consequence, we obtain a formula for the number of such solutions with a fixed number of elements. We also describe some properties of the automorphism groups in this case; in particular, we show they are regular abelian groups.

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19

Bachiller, David, Ferran Cedó, and Leandro Vendramin. "A characterization of finite multipermutation solutions of the Yang-Baxter equation." Publicacions Matemàtiques 62 (July 1, 2018): 641–49. http://dx.doi.org/10.5565/publmat6221809.

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20

Castelli, Marco, Francesco Catino, Maria Maddalena Miccoli, and Giuseppina Pinto. "Dynamical extensions of quasi-linear left cycle sets and the Yang–Baxter equation." Journal of Algebra and Its Applications 18, no. 11 (August 19, 2019): 1950220. http://dx.doi.org/10.1142/s0219498819502207.

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In this paper, we give a characterization of the quasi-linear left cycle sets [Formula: see text] with [Formula: see text] via unitary metahomomorphisms and a complete description of those with [Formula: see text] improving the results obtained in [F. Catino and M. M. Miccoli, Construction of quasi-linear left cycle sets, J. Algebra Appl. 14(1) (2015), Article ID:1550001, 1–7]. Moreover, we develop a theory of dynamical extensions of quasi-linear left cycle sets to provide new set-theoretic solutions of the Yang–Baxter equation that are non-degenerate, involutive and multipermutational.

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21

Kong, Justin. "Ulam Ball Size Analysis for Permutation and Multipermutation Codes Correcting Translocation Errors." IEEE Transactions on Information Theory 65, no. 12 (December 2019): 7806–28. http://dx.doi.org/10.1109/tit.2019.2938987.

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22

Rump, Wolfgang. "Two theorems on balanced braces." Proceedings of the Edinburgh Mathematical Society 64, no. 2 (May 2021): 262–78. http://dx.doi.org/10.1017/s0013091521000134.

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AbstractTwo theorems of Gateva-Ivanova [Set-theoretic solutions of the Yang-Baxter equation, braces and symmetric groups, Adv. Math. 338 (2018), 649–701] on square-free set-theoretic solutions to the Yang–Baxter equation are extended to a wide class of solutions. The square-free hypothesis is almost completely removed. Gateva-Ivanova and Majid's ‘cyclic’ condition ${\boldsymbol {\rm lri}}$ is shown to be equivalent to balancedness, introduced in Rump [A decomposition theorem for square-free unitary solutions of the quantum Yang-Baxter equation, Adv. Math. 193 (2005), 40–55]. Basic results on balanced solutions are established. For example, it is proved that every finite, not necessarily square-free, balanced brace determines a multipermutation solution.

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23

Acri, E., R. Lutowski, and L. Vendramin. "Retractability of solutions to the Yang–Baxter equation and p-nilpotency of skew braces." International Journal of Algebra and Computation 30, no. 01 (September 26, 2019): 91–115. http://dx.doi.org/10.1142/s0218196719500656.

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Using Bieberbach groups, we study multipermutation involutive solutions to the Yang–Baxter equation. We use a linear representation of the structure group of an involutive solution to study the unique product property in such groups. An algorithm to find subgroups of a Bieberbach group isomorphic to the Promislow subgroup is introduced and then used in the case of structure group of involutive solutions. To extend the results related to retractability to non-involutive solutions, following the ideas of Meng, Ballester-Bolinches and Romero, we develop the theory of right [Formula: see text]-nilpotent skew braces. The theory of left [Formula: see text]-nilpotent skew braces is also developed and used to give a short proof of a theorem of Smoktunowicz in the context of skew braces.

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24

Jedlička, Přemysl, Agata Pilitowska, and Anna Zamojska-Dzienio. "The construction of multipermutation solutions of the Yang-Baxter equation of level 2." Journal of Combinatorial Theory, Series A 176 (November 2020): 105295. http://dx.doi.org/10.1016/j.jcta.2020.105295.

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25

Lebed, Victoria, and Leandro Vendramin. "On Structure Groups of Set-Theoretic Solutions to the Yang–Baxter Equation." Proceedings of the Edinburgh Mathematical Society 62, no. 3 (January 11, 2019): 683–717. http://dx.doi.org/10.1017/s0013091518000548.

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AbstractThis paper explores the structure groups G(X,r) of finite non-degenerate set-theoretic solutions (X,r) to the Yang–Baxter equation. Namely, we construct a finite quotient $\overline {G}_{(X,r)}$ of G(X,r), generalizing the Coxeter-like groups introduced by Dehornoy for involutive solutions. This yields a finitary setting for testing injectivity: if X injects into G(X,r), then it also injects into $\overline {G}_{(X,r)}$. We shrink every solution to an injective one with the same structure group, and compute the rank of the abelianization of G(X,r). We show that multipermutation solutions are the only involutive solutions with diffuse structure groups; that only free abelian structure groups are bi-orderable; and that for the structure group of a self-distributive solution, the following conditions are equivalent: bi-orderable, left-orderable, abelian, free abelian and torsion free.

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26

Bachiller, David, Ferran Cedó, Eric Jespers, and Jan Okniński. "A family of irretractable square-free solutions of the Yang–Baxter equation." Forum Mathematicum 29, no. 6 (January 1, 2017). http://dx.doi.org/10.1515/forum-2015-0240.

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AbstractA new family of non-degenerate involutive set-theoretic solutions of the Yang–Baxter equation is constructed. All these solutions are strong twisted unions of multipermutation solutions of multipermutation level at most two. A large subfamily consists of irretractable and square-free solutions. This subfamily includes a recent example of Vendramin [

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27

Rump, Wolfgang. "Classification of Non-Degenerate Involutive Set-Theoretic Solutions to the Yang-Baxter Equation with Multipermutation Level Two." Algebras and Representation Theory, June 8, 2021. http://dx.doi.org/10.1007/s10468-021-10067-5.

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