We introduce $3 $-dimensional generalizations of Postnikov's plabic graphs and use them
to establish cluster structures for type $ A $ braid varieties. Our results include known cluster …

The generalized cluster complex was introduced by Fomin and Reading, as a natural
extension of the Fomin-Zelevinsky cluster complex coming from finite type cluster algebras …

Reading cut the hyperplanes in a real central arrangement $\mathcal H $ into pieces
called\emph {shards}, which reflect order-theoretic properties of the arrangement. We show …

Although both noncrossing partitions and nonnesting partitions are uniformly enumerated for
Weyl groups, the exact relationship between these two sets of combinatorial objects remains …

We give the first type-independent proof of the Kreweras-style formulas for the enumeration
of noncrossing partitions in a real reflection group W, with respect to parabolic type. This …

Assuming standard conjectures, we show that the canonical symmetrizing trace evaluated at
powers of a Coxeter element produces rational Catalan numbers for irreducible spetsial …

I summarize a framework for finding and proving interesting combinatorial formulas using
braid varieties. The combinatorics comes from the Deodhar decomposition of these braid …

We construct a bijection between certain Deodhar components of a braid variety constructed
from an affine Kac-Moody group of type $ A_ {n-1} $ and vertex-labeled trees on $ n …

For each pair of coprime integers $ a $ and $ b $ one defines the" rational $ q $-Catalan
number" $\mathrm {Cat} _q (a, b)=\bigl [\hskip-1.5 pt\begin {smallmatrix}{a-1+ b}\\{a-1}\end …

Fix a multiset ̂S of small steps, and consider all walks W (̂S) from (2, 0) to (− 1, 0) using
the collection of steps in ̂S that avoid the negative x and y axes, except at the final point of …