Sylvie Corteel ; Philippe Nadeau
-
Bijections for Permutation Tableaux
dmtcs:3632 -
Discrete Mathematics & Theoretical Computer Science,
January 1, 2008,
DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008)
-
https://doi.org/10.46298/dmtcs.3632
In this paper we propose a new bijection between permutation tableaux and permutations. This bijection shows how natural statistics on the tableaux are equidistributed to classical statistics on permutations: descents, RL-minima and pattern enumerations. We then use the bijection, and a related encoding of tableaux by words, to prove results about the enumeration of permutations with a fixed number of 31-2 patterns, and to define subclasses of permutation tableaux that are in bijection with set partitions. An extended version of this work is available in [6].
Paweł Hitczenko;Aleksandr Yaroslavskiy, 2020, Asymptotic normality of the number of corners in tableaux associated with the partially asymmetric simple exclusion process, Random Structures and Algorithms, 57, 4, pp. 1248-1271, 10.1002/rsa.20961, https://doi.org/10.1002/rsa.20961.
Soojin Cho;Kyoungsuk Park, 2018, A Combinatorial Proof of a Symmetry of (t, q)-Eulerian Numbers of Type B and Type D, arXiv (Cornell University), 22, 1, pp. 99-134, 10.1007/s00026-018-0372-6, https://arxiv.org/abs/1309.5809.
Xavier Gérard Viennot;Olya Mandelshtam;Xavier Viennot, 2018, Rhombic alternative tableaux and assemblées of permutations, arXiv (Cornell University), 73, pp. 1-19, 10.1016/j.ejc.2018.05.002, https://arxiv.org/abs/1609.07638.
Amanda Lohss, 2016, The asymptotic distribution of symbols on diagonals of random weighted staircase tableaux, arXiv (Cornell University), 49, 4, pp. 795-818, 10.1002/rsa.20665, https://arxiv.org/abs/1512.00329.
Sylvie Corteel;Sandrine Dasse-Hartaut, 2016, A Bijection from Staircase Tableaux to Inversion Tables, Giving Some Eulerian and Mahonian Statistics, Annals of Combinatorics, 20, 4, pp. 737-754, 10.1007/s00026-016-0329-6.
Carol J. Wang;Zhongjin Chen, 2015, The parity of the number of permutation tableaux in a fixed shape, Applied Mathematics and Computation, 265, pp. 1090-1097, 10.1016/j.amc.2015.06.024.
William Y.C. Chen;Lewis H. Liu;Carol J. Wang, 2013, Linked Partitions and Permutation Tableaux, The Electronic Journal of Combinatorics, 20, 3, 10.37236/3408, https://doi.org/10.37236/3408.
Matthieu Josuat-Vergès, 2011, Combinatorics of the Three-Parameter PASEP Partition Function, The Electronic Journal of Combinatorics, 18, 1, 10.37236/509, https://doi.org/10.37236/509.
Philippe Nadeau, 2011, The structure of alternative tableaux, arXiv (Cornell University), 118, 5, pp. 1638-1660, 10.1016/j.jcta.2011.01.012.
Sylvie Corteel;Lauren K. Williams, 2011, Tableaux combinatorics for the asymmetric exclusion process and Askey-Wilson polynomials, arXiv (Cornell University), 159, 3, 10.1215/00127094-1433385, https://arxiv.org/abs/0910.1858.
J. Bell;S. Launois;J. Lutley, 2010, An automaton-theoretic approach to the representation theory of quantum algebras, arXiv (Cornell University), 223, 2, pp. 476-510, 10.1016/j.aim.2009.08.013, https://arxiv.org/abs/0901.4707.