The structure of alternative tableaux

DOI10.1016/j.jcta.2011.01.012zbMath1235.05014arXiv0908.4050OpenAlexW2047135328MaRDI QIDQ533344

Philippe Nadeau

Publication date: 3 May 2011

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0908.4050

zbMATH Keywords

shapepermutationsasymmetric exclusion processpermutation tableauxalternative tableauxalternating treesFerrers diagram

Mathematics Subject Classification ID

Trees (05C05) Exact enumeration problems, generating functions (05A15) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Partitions; congruences and congruential restrictions (11P83)

Related Items (22)

Permutation statistics and weak Bruhat order in permutation tableaux of type \(B\) ⋮ On the combinatorics of symmetrized poly-Bernoulli numbers ⋮ Rhombic alternative tableaux and assemblées of permutations ⋮ The parity of the number of permutation tableaux in a fixed shape ⋮ Bijective enumerations for symmetrized poly-Bernoulli polynomials ⋮ Erratum to ``Tableaux combinatorics for the asymmetric exclusion process and Askey-Wilson polynomials ⋮ Tree-like tableaux ⋮ Combinatorics of non-ambiguous trees ⋮ Context-free grammars, generating functions and combinatorial arrays ⋮ Combinatorics on permutation tableaux of type A and type B ⋮ New interpretations for noncrossing partitions of classical types ⋮ Multivariate Eulerian Polynomials and Exclusion Processes ⋮ Moments of Askey-Wilson polynomials ⋮ Block decomposition and statistics arising from permutation tableaux ⋮ A bijection from staircase tableaux to inversion tables, giving some Eulerian and Mahonian statistics ⋮ A combinatorial proof of a symmetry of \((t,q)\)-Eulerian numbers of type \(B\) and type \(D\) ⋮ The Matrix Ansatz, orthogonal polynomials, and permutations ⋮ Corners in tree-like tableaux ⋮ Combinatorics of faithfully balanced modules ⋮ A generalized Eulerian triangle from staircase tableaux and tree-like tableaux ⋮ Formulae for Askey-Wilson moments and enumeration of staircase tableaux ⋮ Combinatorics of the 2-species exclusion processes, marked Laguerre histories, and partially signed permutations

Cites Work

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• Permutation tableaux and permutation patterns
• A combinatorial approach to jumping particles
• On some properties of permutation tableaux
• Tableaux combinatorics for the asymmetric exclusion process
• Total positivity for cominuscule Grassmannians.
• Bijections for permutation tableaux
• Staircase tableaux, the asymmetric exclusion process, and Askey-Wilson polynomials
• Exact solution of a 1D asymmetric exclusion model using a matrix formulation
• Asymmetric simple exclusion process with open boundaries and Askey–Wilson polynomials
• A Markov Chain on Permutations which Projects to the PASEP

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