8 papers
Note on adjacency spectra for twice punctured hypercubes
Jang Soo Kim, Victor Reiner, Laura Schoenzeit
Eigenspaces of hypercube graph adjacency matrices are well understood. We extend this to subgraphs obtained by removing a vertex or antipodal pair of vertices, motivated by a quest…
Majority relations for Condorcet domains of tiling type
Victor Reiner, Bridget Eileen Tenner
Condorcet domains are subsets of permutations arising in voting theory: regarding their permutations as preference orders on a list of candidates, one avoids Condorcet's paradox wh…
Configuration spaces and peak representations
Marcelo Aguiar, Sarah Brauner, Victor Reiner
Within the group algebras of the symmetric and hyperoctahedral groups, one has their descent algebras and families of Eulerian idempotents. These idempotents are known to generate…
Invariant theory for wreath products acting on superpolynomials
Trevor Karn, Victor Reiner
This paper considers a finite group acting linearly on the variables of a polynomial algebra, or an exterior algebra, or superpolynomial algebra with both commuting and ant…
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…
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…
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…
Chow Rings of Matroids as Permutation Representations
Robert Angarone, Anastasia Nathanson, Victor Reiner
Given a matroid and a group of its matroid automorphisms, we study the induced group action on the Chow ring of the matroid. This turns out to always be a permutation action. Work…