11 citations · 19 across the 8 of their papers we have counts for
8 papers · 1 filter
Combinatorics of Triangular Partitions
François Bergeron, Mikhail Mazin
The aim of this paper is to develop the combinatorics of constructions associated to what we call \emph{triangular partitions}. As introduced in arXiv:2102.07931, these are the par…
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…
Pak-Stanley labeling for Central Graphical Arrangements
Mikhail Mazin, Joshua Miller
The original Pak-Stanley labeling was defined by Pak and Stanley as a bijective map from the set of regions of an extended Shi arrangement to the set of parking functions. This map…
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…
Rational Parking Functions and LLT Polynomials
Eugene Gorsky, Mikhail Mazin
We prove that the combinatorial side of the "Rational Shuffle Conjecture" provides a Schur-positive symmetric polynomial. Furthermore, we prove that the contribution of a given rat…
Multigraph Hyperplane Arrangements and Parking Functions
Mikhail Mazin
Back in the nineties Pak and Stanley introduced a labeling of the regions of a k-Shi arrangement by k-parking functions and proved its bijectivity. Duval, Klivans, and Martin consi…