8 papers
Interval hypergraphic polytopes (or deformed associahedra), Tamari interval posets, and weeping willows
Jose Bastidas, Félix Gélinas, Vincent Pilaud +3
For a hypergraph on , the hypergraphic polytope is the Minkowski sum of the standard simplices for all .…
The graph of implicit edge dependencies for indecomposability and beyond
Arnau Padrol, Germain Poullot
A polytope is called indecomposable if it cannot be expressed nontrivially as a Minkowski sum of other polytopes. Since Gale introduced the concept in 1954, several increasingly st…
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…
Deformation cones of graphical zonotopes for -free graph
Germain Poullot
In this paper, we compute a triangulation of certain faces of the submodular cone. More precisely, graphical zonotopes are generalized permutahedra, and hence their deformation con…