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math.CO2024
Harmonics and graded Ehrhart theory
Victor Reiner, Brendon Rhoades
The Ehrhart polynomial and Ehrhart series count lattice points in integer dilations of a lattice polytope. We introduce and study a -deformation of the Ehrhart series, based on…
math.CO2024
Koszulity, supersolvability, and Stirling representations
Ayah Almousa, Victor Reiner, Sheila Sundaram
Supersolvable hyperplane arrangements and matroids are known to give rise to certain Koszul algebras, namely their Orlik-Solomon algebras and graded Varchenko-Gel'fand algebras. We…
math.CO2024
Sandpile groups for cones over trees
Victor Reiner, Dorian Smith
Sandpile groups are a subtle graph isomorphism invariant, in the form of a finite abelian group, whose cardinality is the number of spanning trees in the graph. We study their grou…