Combinatorial Identities for Vacillating Tableaux
Zhanar Berikkyzy, Pamela E. Harris, Anna Pun, Catherine Yan, Chenchen, Zhao
TL;DR
This paper explores combinatorial identities related to vacillating tableaux, sequences of integer partitions with connections to algebraic and combinatorial structures, providing new enumeration formulas and identities.
Contribution
It introduces new combinatorial identities and enumeration formulas for vacillating tableaux and their variants, advancing understanding of their combinatorial properties.
Findings
Derived multiple combinatorial identities for vacillating tableaux
Established enumeration formulas for simplified and limiting vacillating tableaux
Connected vacillating tableaux to algebraic and combinatorial structures
Abstract
Vacillating tableaux are sequences of integer partitions that satisfy specific conditions. The concept of vacillating tableaux stems from the representation theory of the partition algebra and the combinatorial theory of crossings and nestings of matchings and set partitions. In this paper, we further investigate the enumeration of vacillating tableaux and derive multiple combinatorial identities and integer sequences relating to the number of vacillating tableaux, simplified vacillating tableaux, and limiting vacillating tableaux.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Advanced Mathematical Identities · Algebraic structures and combinatorial models