Wallner, M. (2022, December 7). Young tableaux with periodic walls: counting with the density method [Conference Presentation]. SFB F50 Algorithmic and Enumerative Combinatorics veteran status seminar, Admont, Austria.
E104-05 - Forschungsbereich Kombinatorik und Algorithmen
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Date (published):
7-Dec-2022
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Event name:
SFB F50 Algorithmic and Enumerative Combinatorics veteran status seminar
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Event date:
5-Dec-2022 - 7-Dec-2022
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Event place:
Admont, Austria
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Keywords:
Young tableaux, analytic combinatorics, generating functions, D-finite functions, hypergeometric functions, differentially-algebraic functions, random generation, density method, linear extensions of posets
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Abstract:
We consider a generalization of Young tableaux in which we allow some consecutive pairs of cells with decreasing labels, conveniently visualized by a "wall" between the corresponding cells. Some shapes can be enumerated by variants of hook-length type formulas. We focus on families of tableaux (like the so-called "Jenga tableaux") having some periodic shapes, for which the generating functions are harder to obtain. We get some interesting new classes of recurrences, and a surprisingly rich zoo of generating functions (algebraic, hypergeometric, D-finite, differentially-algebraic). Some patterns lead to nice bijections with trees, lattice paths, or permutations. Our approach relies on the density method, a powerful way to perform both random generation and enumeration of linear extensions of posets.
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Project title:
Gestreckte Exponenten und darüber hinaus: P 34142-N (Fonds zur Förderung der wissenschaftlichen Forschung (FWF)) Funktionsgleichungen für Gitter- und Baumstrukturen: J4162-N35 (Fonds zur Förderung der wissenschaftlichen Forschung (FWF))
