7 papers
Coxeter and Schubert combinatorics of -Involutions
Jack Chen-An Chou, Zachary Hamaker
The variety of complete quadrics is the wonderful compactification of and admits a cell decomposition into Borel orbits indexed by combinatorial objects called -invo…
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…
Odd Shifted Parking Functions
Zachary Hamaker, Jesse Kim
Stanley recently introduced the shifted parking function symmetric function , which is the shiftification of Haiman's parking function symmetric function . The function…
Moments of permutation statistics by cycle type
Zachary Hamaker, Brendon Rhoades
Beginning with work of Zeilberger on classical pattern counts, there are a variety of structural results for moments of permutation statistics applied to random permutations. Using…
Partial permutations and character evaluations
Zachary Hamaker, Brendon Rhoades
Let and be two length sequences drawn from . We have the group algebra element $[I,J] := \sum_{w(I) = J} w \in…
Type C -Stanley symmetric functions and KraÅkiewicz-Hecke insertion
Joshua Arroyo, Zachary Hamaker, Graham Hawkes +1
We study Type C -Stanley symmetric functions, which are -theoretic extensions of the Type C Stanley symmetric functions. They are indexed by signed permutations and can be us…