5 citations · 8 across the 9 of their papers we have counts for
14 papers
Inscribable Fans II: Inscribed zonotopes, simplicial arrangements, and reflection groups
Sebastian Manecke, Raman Sanyal
An arrangement of hyperplanes is strongly inscribable if it has an inscribed (or ideal hyperbolic) zonotope. We characterize inscribed zonotopes and prove that the family of strong…
The Polyhedral Geometry of Pivot Rules and Monotone Paths
Alexander E. Black, Jesús A. De Loera, Niklas Lütjeharms +1
Motivated by the analysis of the performance of the simplex method we study the behavior of families of pivot rules of linear programs. We introduce normalized-weight pivot rules w…
Fan Valuations and spherical intrinsic volumes
Spencer Backman, Sebastian Manecke, Raman Sanyal
We generalize valuations on polyhedral cones to valuations on fans. For fans induced by hyperplane arrangements, we show a correspondence between rotation-invariant valuations and…
Coprime Ehrhart theory and counting free segments
Sebastian Manecke, Raman Sanyal
A lattice polytope is "free" (or "empty") if its vertices are the only lattice points it contains. In the context of valuation theory, Klain (1999) proposed to study the functions…
Tropical Carathéodory with Matroids
Georg Loho, Raman Sanyal
Bárány's colorful generalization of Carathéodory's Theorem combines geometrical and combinatorial constraints. Kalai-Meshulam (2005) and Holmsen (2016) generalized Bárány's theorem…
Standard complexes of matroids and lattice paths
Alexander Engström, Raman Sanyal, Christian Stump
Motivated by Gröbner basis theory for finite point configurations, we define and study the class of "standard complexes" associated to a matroid. Standard complexes are certain sub…