7 papers
Volume and Projection Inequalities I: Zonoids and Courtade's Conjecture
Matthieu Fradelizi, Alfredo Hubard, Auttawich Manui +3
We study volume and projection inequalities for zonoids through the multiaffine determinant polynomials that encode their volumes. We show that a log-submodularity conjecture for t…
Matroid flat counts can have many peaks
Alexander Divoux, Matt Larson, Chayim Lowen +1
We disprove Rota's conjecture that the counts of flats in a matroid according to rank form a unimodal sequence. Furthermore, we show that this sequence can have arbitrarily many pe…
Matroid flat counts are not unimodal
Alexander Divoux, Chayim Lowen, Shouda Wang
We give counterexamples to Rota's 1970 conjecture that the sequence counting flats of varying rank in a matroid is unimodal. More specifically, inspired by Larson's recent disproof…
A complete solution to the Grünbaum--Loewner centroid problems
Xiong Ge, Wang Shouda, Yang Kai-Wen +1
In the 1960s, Grünbaum and Loewner raised problems concerning the minimum possible number of hyperplane sections of a convex body in whose centroids coincide with the centro…
Monotonicity of the deficit in the local log-Brunn-Minkowski inequality
Shouda Wang
We establish a monotonicity property of the deficit associated with the local log-Brunn-Minkowski inequality (LLBM) under addition of line segments. As a corollary, if the LLBM hol…
On Minkowski's monotonicity problem
Ramon van Handel, Shouda Wang
We address an old open question in convex geometry that dates back to the work of Minkowski: what are the equality cases of the monotonicity of mixed volumes? The problem is equiva…