Results 11 to 20 of about 11,311 (139)
A simple bijection between permutation tableaux and permutations
, 2006 We present a simple a bijection between permutations of $\{1,..., n\}$ with $k$ descents and permutation tableaux of length $n$ with $k ...
Corteel, Sylvie
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Marking Algorithms in Permutation Tableaux and Transformations on Linked Partitions
MathematicsIn this paper, we focus on the internal structural characteristics of permutation tableaux and their correspondence with linked partitions. We begin by introducing new statistics for permutation tableaux, designed to thoroughly describe various ...
Carol Jian Wang, Meryl Nan Wang
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Linked Partitions and Permutation Tableaux [PDF]
The Electronic Journal of Combinatorics, 2013 Linked partitions were introduced by Dykema in the study of transforms in free probability theory, whereas permutation tableaux were introduced by Steingrímsson and Williams in the study of totally positive Grassmannian cells. Let $[n]=\{1,2,\ldots,n\}$. Let $L(n,k)$ denote the set of linked partitions of $[n]$ with $k$ blocks, let $P(n,k)$ denote the
William Y. C. Chen +2 more
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Refined Enumeration of Corners in Tree-like Tableaux [PDF]
Discrete Mathematics & Theoretical Computer Science, 2017 Tree-like tableaux are certain fillings of Ferrers diagrams originally introduced by Aval et al., which are in simple bijections with permutation tableaux coming from Postnikov's study of totally nonnegative Grassmanian and alternative tableaux ...
Sherry H. F. Yan, Robin D. P. Zhou
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Permutations with short monotone subsequences [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 We consider permutations of $1,2,...,n^2$ whose longest monotone subsequence is of length $n$ and are therefore extremal for the Erdős-Szekeres Theorem. Such permutations correspond via the Robinson-Schensted correspondence to pairs of square $n \times n$
Dan Romik
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Permutation Tableaux and the Dashed Permutation Pattern 32–1 [PDF]
The Electronic Journal of Combinatorics, 2011 We give a solution to a problem posed by Corteel and Nadeau concerning permutation tableaux of length $n$ and the number of occurrences of the dashed pattern 32–1 in permutations on $[n]$. We introduce the inversion number of a permutation tableau. For a permutation tableau $T$ and the permutation $\pi$ obtained from $T$ by the bijection of Corteel ...
William Y. C. Chen, Lewis H. Liu
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Generating trees for partitions and permutations with no k-nestings [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 We describe a generating tree approach to the enumeration and exhaustive generation of k-nonnesting set partitions and permutations. Unlike previous work in the literature using the connections of these objects to Young tableaux and restricted lattice ...
Sophie Burrill +3 more
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Rhombic alternative tableaux and assemblées of permutations [PDF]
European Journal of Combinatorics, 2018 In this paper, we introduce the rhombic alternative tableaux, whose weight generating functions provide combinatorial formulae to compute the steady state probabilities of the two-species ASEP. In the ASEP, there are two species of particles, one heavy and one light, hopping right and left on a one-dimensional finite lattice with open boundaries ...
Olya Mandelshtam, Xavier Gérard Viennot
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Generalized triangulations, pipe dreams, and simplicial spheres [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 We exhibit a canonical connection between maximal $(0,1)$-fillings of a moon polyomino avoiding north-east chains of a given length and reduced pipe dreams of a certain permutation.
Luis Serrano, Christian Stump
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Matrix Ansatz, lattice paths and rook placements [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 We give two combinatorial interpretations of the Matrix Ansatz of the PASEP in terms of lattice paths and rook placements. This gives two (mostly) combinatorial proofs of a new enumeration formula for the partition function of the PASEP.
S. Corteel +3 more
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