Christopher R. H. Hanusa

The enumeration of fully commutative affine permutations

We give a generating function for the fully commutative affine permutations enumerated by rank and Coxeter length, extending formulas due to Stembridge and Barcucci-Del Lungo-Pergola-Pinzani. For fixed rank, the length generating functions have coefficients that are periodic with period dividing the rank. In the course of proving these formulas, we obtain results that elucidate the structure of the fully commutative affine permutations.

Combinatorics of the zeta map on rational Dyck paths

An

Determinants in the Kronecker product of matrices: the incidence matrix of a complete graph

(a,b)

Nonattacking Queens in a Rectangular Strip

-Dyck path

Ensuring every candidate wins under positional voting

P

Note: Applying a combinatorial determinant to count weighted cycle systems in a directed graph

is a lattice path from

Solving multivariate functional equations

(0,0)

Results and conjectures on simultaneous core partitions

to

Abacus models for parabolic quotients of affine Weyl groups

(b,a)

A

that stays above the line