We study here the Super Nabla operator, which is shown to be generic among operators for
which the modified Macdonald polynomials are joint eigenfunctions. All known such …

The purpose of this paper is to present conjectures that extend to any “triangular” partitions
(partitions “under any line” in the terminology of Blasiak-Haiman-Morse-Pun-Seelinger) …

We introduce the higher rank $(q, t) $-Catalan polynomials and prove they equal truncations
of the Hikita polynomial to a finite number of variables. Using affine compositions and a …

Abstract We compute the Borel–Moore homology of unramified affine Springer fibers for
under the assumption that they are equivariantly formal and relate them to certain ideals …

We introduce a family of generalized Schr\" oder polynomials $ S_\tau (q, t, a) $, indexed by
triangular partitions $\tau $ and prove that $ S_\tau (q, t, a) $ agrees with the Poincar\'e …

I present an overview of the research I have conducted for the past ten years in algebraic,
bijective, enumerative, and geometric combinatorics. The two main objects I have studied …

A triangular partition is a partition whose Ferrers diagram can be separated from its
complement (as a subset of $\mathbb {N}^ 2$) by a straight line. Having their origins in …

We compute the Borel-Moore homology of unramified affine Springer fibers for $\mathrm
{GL} _n $ under the assumption that they are equivariantly formal and relate them to certain …

We study the (q, t)-enumeration of triangular Dyck paths considered by Bergeron and Mazin.
To do so, we introduce the notion of triangular and sim-sym tableaux and the deficit statistic …

An integer partition is said to be triangular if its Ferrers diagram can be separated from its
complement by a straight line. This work builds on some recent developments on the topic in …