102 citations · 111 across the 13 of their papers we have counts for
9 papers · 1 filter
Higher rank -Catalan polynomials, affine Springer fibers, and a finite Rational Shuffle Theorem
Nicolle González, José Simental, Monica Vazirani
We introduce the higher rank -Catalan polynomials and prove they equal truncations of the Hikita polynomial to a finite number of variables. Using affine compositions and a…
Recursions for rational q,t-Catalan numbers
Eugene Gorsky, Mikhail Mazin, Monica Vazirani
We give a simple recursion labeled by binary sequences which computes rational -Catalan power series, both in relatively prime and non relatively prime cases. It is inspired b…
Rational Dyck Paths in the Non Relatively Prime Case
Eugene Gorsky, Mikhail Mazin, Monica Vazirani
We study the relationship between rational slope Dyck paths and invariant subsets of extending the work of the first two authors in the relatively prime case. We also…
Affine permutations and rational slope parking functions
Eugene Gorsky, Mikhail Mazin, Monica Vazirani
We introduce a new approach to the enumeration of rational slope parking functions with respect to the area and a generalized dinv statistics, and relate the combinatorics of parki…
Counting Shi regions with a fixed separating wall
Susanna Fishel, Eleni Tzanaki, Monica Vazirani
Athanasiadis introduced separating walls for a region in the extended Shi arrangement and used them to generalize the Narayana numbers. In this paper, we fix a hyperplane in the ex…
Deformations of permutation representations of Coxeter groups
Eric M. Rains, Monica J. Vazirani
The permutation representation afforded by a Coxeter group W acting on the cosets of a standard parabolic subgroup inherits many nice properties from W such as a shellable Bruhat o…