34 citations · 193 across the 23 of their papers we have counts for
4 papers · 2 filters
Derivatives of Schubert polynomials and proof of a determinant conjecture of Stanley
Zachary Hamaker, Oliver Pechenik, David E Speyer +1
We study the action of a differential operator on Schubert polynomials. Using this action, we first give a short new proof of an identity of I. Macdonald (1991). We then prove a de…
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…
Atoms for signed permutations
Zachary Hamaker, Eric Marberg
There is a natural analogue of weak Bruhat order on the involutions in any Coxeter group. The saturated chains of intervals in this order correspond to reduced words for a certain…