11 citations · 11 across the 10 of their papers we have counts for
6 papers · 1 filter
Higher-order Godbersen inequality and a characterization of simplices via the face lattice
Filip Fryš, Jan Kotrbatý, Mohamed A. Mouamine +1
We settle the long-standing Godbersen conjecture that the mixed volume of a convex body of fixed positive volume with its reflection about the origin is maximized precisely by simp…
The Bézout inequality for mixed volumes characterizes simplices
Dylan Langharst, Shouda Wang
We prove that the Bézout inequality for mixed volumes characterizes simplices among full dimensional convex bodies in every dimension, resolving a conjecture of Soprunov and Zvavit…
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…
A complete solution to the Grünbaum--Loewner centroid problems
Wang Shouda, Xiong Ge, Yang Kaiwen
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 centroi…
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…