5 papers
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…
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…