34 citations · 193 across the 23 of their papers we have counts for
29 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 -invol…
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 Kraśkiewicz-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…
Tableau formula for vexillary double Edelman--Greene coefficients
Adam Gregory, Zachary Hamaker, Tianyi Yu
Lam, Lee and Shimozono recently introduced backstable double Grothendieck polynomials to represent -theory classes of the infinite flag variety. They used them to define double…
Dual Schubert polynomials via a Cauchy identity
Zachary Hamaker
We give a combinatorial proof that Postnikov and Stanley's formula for dual Schubert polynomials in terms of weighted chains in Bruhat order is equivalent to a classical Cauchy ide…
Lenart's bijection via bumpless pipe dreams
Adam Gregory, Zachary Hamaker
Pipe dreams and bumpless pipe dreams for vexillary permutations are each known to be in bijection with certain semistandard tableaux via maps due to Lenart and Weigandt, respective…
Characters of local and regular permutation statistics
Zachary Hamaker, Brendon Rhoades
The goal of this monograph is to study the indicator function for a set of permutations mapping one finite sequence of positive integers to another from a representation theoretic,…
Three coloring via triangle counting
Zachary Hamaker, Vincent Vatter
In the first partial result toward Steinberg's now-disproved three coloring conjecture, Abbott and Zhou used a counting argument to show that every planar graph without cycles of l…
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…
On pattern avoidance in matchings and involutions
Jonathan J. Fang, Zachary Hamaker, Justin M. Troyka
We study the relationship between two notions of pattern avoidance for involutions in the symmetric group and their restriction to fixed-point-free involutions. The first is classi…
Gröbner geometry of Schubert polynomials through ice
Zachary Hamaker, Oliver Pechenik, Anna Weigandt
The geometric naturality of Schubert polynomials and their combinatorial pipe dream representations was established by Knutson and Miller (2005) via antidiagonal Gröbner degenerati…
Involution pipe dreams
Zachary Hamaker, Eric Marberg, Brendan Pawlowski
Involution Schubert polynomials represent cohomology classes of -orbit closures in the complete flag variety, where is the orthogonal or symplectic group. We show they also…
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…
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…
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…
Fixed-point-free involutions and Schur P-positivity
Zachary Hamaker, Eric Marberg, Brendan Pawlowski
The orbits of the symplectic group acting on the type A flag variety are indexed by the fixed-point-free involutions in a finite symmetric group. The cohomology classes of the clos…
Schur P-positivity and involution Stanley symmetric functions
Zachary Hamaker, Eric Marberg, Brendan Pawlowski
The involution Stanley symmetric functions are the stable limits of the analogues of Schubert polynomials for the orbits of the orthogonal group in the flag variety. Th…
Transition formulas for involution Schubert polynomials
Zachary Hamaker, Eric Marberg, Brendan Pawlowski
The orbits of the orthogonal and symplectic groups on the flag variety are in bijection, respectively, with the involutions and fixed-point-free involutions in the symmetric group…
Doppelgängers: Bijections of Plane Partitions
Zachary Hamaker, Rebecca Patrias, Oliver Pechenik +1
We say two posets are "doppelgängers" if they have the same number of -partitions of each height . We give a uniform framework for bijective proofs that posets are doppelgäng…