We consider the construction of refined Chern–Simons torus knot invariants by M. Aganagic
and S. Shakirov from the DAHA viewpoint of I. Cherednik. We give a proof of Cherednik's …

We conjecturally extract the triply graded Khovanov–Rozansky homology of the (m, n) torus
knot from the unique finite-dimensional simple representation of the rational DAHA of type A …

The “classical” parking functions, counted by the Cayley number (n+ 1) n− 1, carry a natural
permutation representation of the symmetric group S n in which the number of orbits is the …

We relate the mixed Hodge structure on the cohomology of open positroid varieties (in
particular, their Betti numbers over $\mathbb {C} $ and point counts over $\mathbb {F} _q $) …

Compactified Jacobians and q,t-Catalan numbers, I Page 1 Journal of Combinatorial Theory,
Series A 120 (2013) 49–63 Contents lists available at SciVerse ScienceDirect Journal of …

We introduce a new approach to the enumeration of rational slope parking functions with
respect to the $\operatorname {area} $ and a generalized $\operatorname {dinv} $ statistics …

We observe that for a and b relatively prime, the" abacus construction" identifies the set of
simultaneous (a, b)-core partitions with lattice points in a rational simplex. Furthermore …

We consider two motivic generating functions defined on a variety, and reveal their tight
connection. They essentially count torsion-free bundles and zero-dimensional sheaves. On …

The theory of DAHA-Jones polynomials is extended from torus knots to their arbitrary
iterations (for any reduced root systems and weights), which includes the polynomiality …

We define a family of maps on lattice paths, called sweep maps, that assign levels to each
step in the path and sort steps according to their level. Surprisingly, although sweep maps …