We conjecture two combinatorial interpretations for the symmetric function $\Delta _ {e_k}
e_n $, where $\Delta _f $ is an eigenoperator for the modified Macdonald polynomials …

The notion of parking functions was introduced by Konheim and Weiss [53] as a colorful way
to describe their work on computer storage. The parking problem can be stated as follows …

In 2008, Haglund et al. formulated a Compositional form of the Shuffle Conjecture of
Haglund et al.. In very recent work, Gorsky and Negut, by combining their discoveries [,,] with …

An n-core partition is an integer partition whose Young diagram contains no hook lengths
equal to n. We consider partitions that are simultaneously a-core and b-core for two …

We solve two open problems in Coxeter-Catalan combinatorics. First, we introduce a family
of rational noncrossing objects for any finite Coxeter group, using the combinatorics of …

For any finite path $ v $ on the square grid consisting of north and east unit steps, starting at
(0, 0), we construct a poset Tam $(v) $ that consists of all the paths weakly above $ v $ with …

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 introduce new families of combinatorial objects whose enumeration computes volumes
of flow polytopes. These objects provide an interpretation, based on parking functions, of …

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 …

The Catalan numbers constitute one of the most important sequences in combinatorics.
Catalan objects have been generalized in various directions, including the classical Fuss …