Results 21 to 30 of about 11,311 (139)
Parabolic Catalan numbers count flagged Schur functions and their appearances as type A Demazure characters (key polynomials) [PDF]
Discrete Mathematics & Theoretical Computer Science, 2017 Fix an integer partition lambda that has no more than n parts. Let beta be a weakly increasing n-tuple with entries from {1,..,n}. The flagged Schur function indexed by lambda and beta is a polynomial generating function in x_1, .., x_n for certain ...
Robert A. Proctor, Matthew J. Willis
doaj +1 more source
Inversion Polynomials for Permutations Avoiding Consecutive Patterns [PDF]
, 2014 In 2012, Sagan and Savage introduced the notion of $st$-Wilf equivalence for a statistic $st$ and for sets of permutations that avoid particular permutation patterns which can be extended to generalized permutation patterns.
Cameron, Naiomi, Killpatrick, Kendra
core +1 more source
Alternating Permutations with Restrictions and Standard Young Tableaux [PDF]
The Electronic Journal of Combinatorics, 2012 In this paper, we establish bijections between the set of 4123-avoiding down-up alternating permutations of length $2n$ and the set of standard Young tableaux of shape $(n,n,n)$, and between the set of 4123-avoiding down-up alternating permutations of length $2n-1$ and the set of shifted standard Young tableaux of shape $(n+1, n, n-1)$ via an ...
Yuexiao Xu, Sherry H. F. Yan
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RSK Tableaux and the Weak Order on Fully Commutative Permutations
The Electronic Journal of Combinatorics, 2023 For each fully commutative permutation, we construct a “boolean core,” which is the maximal boolean permutation in its principal order ideal under the right weak order. We partition the set of fully commutative permutations into the recently defined crowded and uncrowded elements, distinguished by whether or not their RSK insertion tableaux satisfy a ...
Emily Gunawan +3 more
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On Some Properties of Permutation Tableaux [PDF]
Annals of Combinatorics, 2007 13 ...
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Rhombic alternative tableaux, assemblees of permutations, and the ASEP [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 In this paper, we introduce therhombic alternative tableaux, whose weight generating functions providecombinatorial formulae to compute the steady state probabilities of the two-species ASEP. In the ASEP, there aretwo species of particles, oneheavyand onelight, on a one-dimensional finite lattice with open boundaries, and theparametersα,β, andqdescribe
Olya Mandelshtam, Xavier Viennot
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The Robinson-Schensted Correspondence and $A_2$-web Bases [PDF]
, 2015 We study natural bases for two constructions of the irreducible representation of the symmetric group corresponding to $[n,n,n]$: the {\em reduced web} basis associated to Kuperberg's combinatorial description of the spider category; and the {\em left ...
Housley, Matthew +2 more
core +4 more sources
Modules of the 0-Hecke algebra arising from standard permuted composition tableaux [PDF]
Journal of Combinatorial Theory, Series A, 2021 We study the $H_n(0)$-module $\mathbf{S}^σ_α$ due to Tewari and van Willigenburg, which was constructed using new combinatorial objects called standard permuted composition tableaux and decomposed into cyclic submodules. First, we show that every direct summand appearing in their decomposition is indecomposable and characterize when $\mathbf{S}^σ_α$ is
Seung-Il Choi +3 more
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The Matrix Ansatz, Orthogonal Polynomials, and Permutations [PDF]
, 2010 In this paper we outline a Matrix Ansatz approach to some problems of combinatorial enumeration. The idea is that many interesting quantities can be expressed in terms of products of matrices, where the matrices obey certain relations. We illustrate this
Corteel, Sylvie +2 more
core +4 more sources
Promotion on oscillating and alternating tableaux and rotation of matchings and permutations [PDF]
Algebraic Combinatorics, 2020 Using Henriques’ and Kamnitzer’s cactus groups, Schützenberger’s promotion and evacuation operators on standard Young tableaux can be generalised in a very natural way to operators acting on highest weight words in tensor products of crystals. For the crystals corresponding to the vector representations of the symplectic groups, we ...
Pfannerer, Stephan +2 more
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