6 papers
Involutions under Bruhat order and labeled Motzkin Paths
Michael Coopman, Zachary Hamaker
In this note, we introduce a statistic on Motzkin paths that describes the rank generating function of Bruhat order for involutions. Our proof relies on a bijection introduced by P…
Bijecting hidden symmetries for skew staircase shapes
Zachary Hamaker, Alejandro H. Morales, Igor Pak +2
We present a bijection between the set of standard Young tableaux of staircase minus rectangle shape, and the set of marked shifted standard Young tableaux of a certain shifted sha…
Wronskian Appell Polynomials and Symmetric Functions
Niels Bonneux, Zachary Hamaker, John Stembridge +1
We study Wronskians of Appell polynomials indexed by integer partitions. These families of polynomials appear in rational solutions of certain Painlevé equations and in the study o…
Pattern avoidance and quasisymmetric functions
Zachary Hamaker, Brendan Pawlowski, Bruce Sagan
Given a set of permutations Pi, let S_n(Pi) denote the set of permutations in the symmetric group S_n that avoid every element of Pi in the sense of pattern avoidance. Given a subs…
Weak order and descents for monotone triangles
Zachary Hamaker, Victor Reiner
Monotone triangles are a rich extension of permutations that biject with alternating sign matrices. The notions of weak order and descent sets for permutations are generalized here…
Relating Edelman-Greene insertion to the Little map
Zachary Hamaker, Benjamin Young
The Little map and the Edelman-Greene insertion algorithm, a generalization of the Robinson-Schensted correspondence, are both used for enumerating the reduced decompositions of an…