M. Gillespie

math.CO2017

Shifted tableaux crystals

Maria Gillespie, Jake Levinson, Kevin Purbhoo

We introduce coplactic raising and lowering operators $E_{i}^{'}$ , $F_{i}^{'}$ , $E_{i}$ , and $F_{i}$ on shifted skew semistandard tableaux. We show that the primed operators and unprimed operato…

math.CO2017

A crystal-like structure on shifted tableaux

Maria Gillespie, Jake Levinson, Kevin Purbhoo

We introduce coplactic raising and lowering operators $E_{i}^{'}$ , $F_{i}^{'}$ , $E_{i}$ , and $F_{i}$ on shifted skew semistandard tableaux. We show that the primed operators and unprimed operato…

math.CO2015

A combinatorial approach to the q,t-symmetry relation in Macdonald polynomials

Maria Monks Gillespie

Using the combinatorial formula for the transformed Macdonald polynomials of Haglund, Haiman, and Loehr, we investigate the combinatorics of the symmetry relation $\widetilde{H}_μ(…