160 citations · 693 across the 40 of their papers we have counts for
12 papers · 1 filter
Random Walks, Equidistribution and Graphical Designs
Stefan Steinerberger, Rekha R. Thomas
Let be a -regular graph on vertices and let be a probability measure on . The act of moving to a randomly chosen neighbor leads to a sequence of probabili…
Graphical Designs and Gale Duality
Catherine Babecki, Rekha R. Thomas
A graphical design is a subset of graph vertices such that the weighted averages of certain graph eigenvectors over the design agree with their global averages. We use Gale duality…
Tropicalization of Graph Profiles
Grigoriy Blekherman, Annie Raymond, Mohit Singh +1
A graph profile records all possible densities of a fixed finite set of graphs. Profiles can be extremely complicated; for instance the full profile of any triple of connected grap…
Simple Graph Density Inequalities with no Sum of Squares Proofs
Grigoriy Blekherman, Annie Raymond, Mohit Singh +1
Establishing inequalities among graph densities is a central pursuit in extremal combinatorics. A standard tool to certify the nonnegativity of a graph density expression is to wri…
Projectively unique polytopes and toric slack ideals
João Gouveia, Antonio Macchia, Rekha R. Thomas +1
The slack ideal of a polytope is a saturated determinantal ideal that gives rise to a new model for the realization space of the polytope. The simplest slack ideals are toric and h…
The Slack Realization Space of a Polytope
João Gouveia, Antonio Macchia, Rekha R. Thomas +1
In this paper we introduce a natural model for the realization space of a polytope up to projective equivalence which we call the slack realization space of the polytope. The model…