The main objects of noncrossing Catalan combinatorics associated to a finite Coxeter
system are noncross-ing partitions, sortable elements, and cluster complexes. The first and …

Recent work of the first author, Negut, and Rasmussen, and of Oblomkov and Rozansky in
the context of Khovanov–Rozansky knot homology produces a family of polynomials in q …

The notion of (a, b)-cores is closely related to rational (a, b)-Dyck paths via the bijection due
to J. Anderson, and thus the number of (a, a+ 1)-cores is given by the Catalan number C a …

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 …

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 …

We construct a family of S n modules indexed by c∈{1,…, n} with the property that upon
restriction to S n− 1 they recover the classical parking function representation of Haiman …

This chapter gives an expository account of some unexpected connections which have
arisen over the last few years between Macdonald polynomials, invariants of torus knots …

The theory of s-core partitions, integer partitions whose hook sets avoid hooks of length s,
lies at the intersection of a surprising number of fields, including number theory …

Recent work of the first author, Negut, and Rasmussen, and of Oblomkov and Rozansky in
the context of Khovanov–Rozansky knot homology produces a family of polynomials in q …

• In 1988, Macdonald [Mac88] introduced a family of symmetric functions Pλ (X; q, t) that
depended on parameters q and t and a family of non-symmetric polynomials Eα (X; q, t) …