4 papers
Many rays of the submodular cone
Georg Loho, Arnau Padrol, Germain Poullot
The study of the cone of submodular functions goes back to Jack Edmonds' seminal 1970 paper, which already highlighted the difficulty of characterizing its extreme rays. Since then…
Ehrhart non-positivity and unimodular triangulations for classes of s-lecture hall simplices
Jhon B. Caicedo, Martina Juhnke, Germain Poullot
Counting lattice points and triangulating polytopes is a prominent subject in discrete geometry, yet proving Ehrhart positivity or existence of unimodular triangulations remain of…
Vertices of the monotone path polytopes of hypersimplicies
Germain Poullot
The monotone path polytope of a polytope encapsulates the combinatorial behavior of the shadow vertex rule (a pivot rule used in linear programming) on . Computing monotone…
Pivot polytopes of products of simplices and shuffles of associahedra
Vincent Pilaud, Germain Poullot
We provide a piecewise linear isomorphism from the normal fan of the pivot polytope of a product of simplices to the normal fan of a shuffle of associahedra.