9 citations · 10 across the 11 of their papers we have counts for
12 papers
Sylvester simplices: Triangulations and Ehrhart-theoretic aspects
Jhon B. Caicedo, Federico Castillo, Martina Juhnke +1
The Sylvester simplex is a -dimensional lattice simplex with exactly interior lattice points. Sylvester simplices are conjectured to be the volume maximi…
Hamiltonicity of graphs of acyclic orientations and acyclic polynomials
Leonie Mühlherr, Germain Poullot
We study the graph of acyclic orientations of a graph . Two acyclic orientations are adjacent in this graph if they disagree on the orientation of a single arc…
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…
Unimodality of the number of paths per length on polytopes: Examples, counterexamples, and a central limit theorem
Martina Juhnke, Germain Poullot
Because of its importance in combinatorics and optimization we study the full distribution of the lengths of monotone paths of a convex polytope. De Loera had conjectured that the…
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.
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…
Deformed graphical zonotopes
Arnau Padrol, Vincent Pilaud, Germain Poullot
We study deformations of graphical zonotopes. Deformations of the classical permutahedron (which is the graphical zonotope of the complete graph) have been intensively studied in r…
Deformation cones of graph associahedra and nestohedra
Arnau Padrol, Vincent Pilaud, Germain Poullot
We give the facet description of the deformation cones of graph associahedra and nestohedra, generalizing the classical parametrization of the family of deformed permutahedra by th…