14 citations · 29 across the 12 of their papers we have counts for
13 papers
An involution on Dyck paths in the region $\defc\le\min(\area,\dinv)$ that interchanges area and dinv
Graham Hawkes
We construct an explicit involution on Dyck paths satisfying $\defc\le\min(\area,\dinv)$ that interchanges area and dinv, where $\defc=\binom n2-\area-\dinv$ and is the semilen…
Dyck Symmetric Functions and Applications to \(q,t\)-Catalan Polynomials
Graham Hawkes
This paper develops three related combinatorial results for Dyck-type sequences. First, it constructs a row-insertion algorithm for dual Dyck sequences and extends it to Dyck table…
A conjectured formula for the rational -Catalan polynomial
Graham Hawkes
We conjecture a formula for the rational -Catalan polynomial that is symmetric in and by definition. The conjecture posits that …
Unified framework for tableau models of Grothendieck polynomials
Graham Hawkes
We give combinatorial proofs of two types of duality for Grothendieck polynomials by constructing a unified combinatorial framework incorporating set-valued tableaux, musltiset-val…
Combinatorics of Double Grothendieck Polynomials
Graham Hawkes
We give a proof of the generalized Cauchy identity for double Grothendieck polynomials, a combinatorial interpretation of the stable double Grothendieck polynomials in terms of tri…
-Schur positive -Grothendieck Polynomials
Graham Hawkes
The symmetric Grothendieck polynomials generalize Schur polynomials and are Schur-positive by degree. Combinatorially this is manifested as the generalization of semistandard Young…
Crystal structures for canonical Grothendieck functions
Graham Hawkes, Travis Scrimshaw
We give a -crystal structure on multiset-valued tableaux, hook-valued tableaux, and valued-set tableaux, whose generating functions are the weak symmetric, ca…
Generalized -Catalan numbers
Eugene Gorsky, Graham Hawkes, Anne Schilling +1
Recent work of the first author, Negut and Rasmussen, and of Oblomkov and Rozansky in the context of Khovanov--Rozansky knot homology produces a family of polynomials in and $t…
Characterization of queer supercrystals
Maria Gillespie, Graham Hawkes, Wencin Poh +1
We provide a characterization of the crystal bases for the quantum queer superalgebra recently introduced by Grantcharov et al.. This characterization is a combination of local que…
Generalized Staircase Tableaux: Symmetry and Applications
Graham Hawkes
We define a number of related combinatorial objects, each of which possesses a surprising symmetry. We include several applications such as a combinatorial explanation for certain…
Crystal Structures for Double Stanley Symmetric Functions
Graham Hawkes
We relate the combinatorial definitions of the type and type Stanley symmetric functions, via a combinatorially defined "double Stanley symmetric function," which gives…
Crystal analysis of type Stanley symmetric functions
Graham Hawkes, Kirill Paramonov, Anne Schilling
Combining results of T.K. Lam and J. Stembridge, the type Stanley symmetric function , indexed by an element in the type Coxeter group, has a nonnega…
An Elementary Proof of the Hook Content Formula
Graham Hawkes
In this paper we prove the Hook Content Formula (HCF) (and Hook Length Formula (HLF)) using induction. Instead of working with Young tableaux directly, we introduce a vector notati…