4 papers
Pattern expansions of permutation statistics
Ian Cavey, Hugh Dennin, Bridget Eileen Tenner
We study the expansions of permutation statistics in the basis of functions counting occurrences of a fixed pattern in a permutation. We show the finiteness of these pattern expans…
Graded Ehrhart theory and toric geometry
Ian Cavey
We give two new constructions of the harmonic algebra of a lattice polytope , a bigraded algebra whose character is the -Ehrhart series of defined by Reiner and Rhoades.…
Domino Tilings, Domino Shuffling, and the Nabla Operator
Ian Cavey, Yi-Lin Lee
We study domino tilings of certain regions , indexed by partitions , weighted according to generalized area and dinv statistics. These statistics arise from the -Catal…
Effective divisors and Newton-Okounkov bodies of Hilbert schemes of points on toric surfaces
Ian Cavey
We compute the (unbounded) Newton-Okounkov body of the Hilbert scheme of points on . We obtain an upper bound for the Newton-Okounkov body of the Hilbert scheme of poi…