11 citations · 17 across the 6 of their papers we have counts for
9 papers
Structures in HOMFLY-PT homology
Alex Chandler, Eugene Gorsky
We study the structure of triply graded Khovanov-Rozansky homology using both the data recently computed by Nakagane and Sano for knots up to 11 crossings, and the $\mathfrak{sl}(2…
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…
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…
Compactified Jacobians and q,t-Catalan numbers, II
Evgeny Gorsky, Mikhail Mazin
We continue the study of the rational-slope generalized -Catalan numbers . We describe generalizations of the bijective constructions of J. Haglund and N. Loehr…
A braid group action on parking functions
Evgeny Gorsky, Mikhail Gorsky
We construct an action of the braid group on strands on the set of parking functions of cars such that elementary braids have orbits of length 2 or 3. The construction is m…
Compactified Jacobians and q,t-Catalan Numbers, I
E. Gorsky, Mikhail Mazin
J. Piontkowski described the homology of the Jacobi factor of a plane curve singularity with one Puiseux pair. We discuss the combinatorial structure of his answer, in particular,…
Symmetries of some motivic integrals
E. Gorsky
We give an explicit formula for the motivic integrals related to the Milnor number over spaces of parametrised arcs on the plane with fixed tangency orders with the axis. These int…
Motivic integrals and functional equations
E. Gorsky
A functional equation for the motivic integral corresponding to the Milnor number of an arc is derived using the Denef-Loeser formula for the change of variables. Its solution is a…