5 papers
New Approaches to Identities for Vacillating Tableaux
Derek Wu, Catherine Yan
A fundamental identity for the number of vacillating tableaux was originally obtained through the representation theory of partition algebras. We extend this identity to arbitrary…
Primeness of generalized parking functions
Sam Armon, Joanne Beckford, Dillon Hanson +4
Classical parking functions are a generalization of permutations that appear in many combinatorial structures. Prime parking functions are indecomposable components such that any c…
On the Correspondence Between Integer Sequences and Vacillating Tableaux
Zhanar Berikkyzy, Pamela E. Harris, Anna Pun +2
A fundamental identity in the representation theory of the partition algebra is for , where ranges over integer partitions of , is t…
Gončarov Polynomials in Partition Lattices and Exponential Families
Ayomikun Adeniran, Catherine Yan
Classical Gončarov polynomials arose in numerical analysis as a basis for the solutions of the Gončarov interpolation problem. These polynomials provide a natural algebraic tool in…
Mixed Statistics on 01-Fillings of Moon Polyominoes
William Y. C. Chen, Andrew Y. Z. Wang, Catherine H. Yan +1
We establish a stronger symmetry between the numbers of northeast and southeast chains in the context of 01-fillings of moon polyominoes. Let $\M$ be a moon polyomino with rows…