73 citations · 326 across the 36 of their papers we have counts for
35 papers · 1 filter
Indecomposability of 0/1-polytopes
Akihiro Higashitani, Arnau Padrol, Raman Sanyal
We prove that every 0/1-polytope has a unique Minkowski decomposition into indecomposable polytopes, up to translation of summands. The summands lie in pairwise orthogonal subspace…
From linear programming to colliding particles
Alexander E. Black, Niklas Lütjeharms, Raman Sanyal
Although simplices are trivial from a linear optimization standpoint, the simplex algorithm can exhibit quite complex behavior. In this paper we study the behavior of max-slope piv…
Kalai's conjecture for unconditional and locally anti-blocking polytopes
Raman Sanyal, Martin Winter
Kalai's conjecture states that every centrally-symmetric -polytope has at least faces. We give short proofs for two special cases: if is unconditional (that is,…
Underlying Flag Polymatroids
Alexander E. Black, Raman Sanyal
We describe a natural geometric relationship between matroids and underlying flag matroids by relating the geometry of the greedy algorithm to monotone path polytopes. This perspec…
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…
On piecewise-linear homeomorphisms between distributive and anti-blocking polyhedra
Christoph Pegel, Raman Sanyal
Stanley (1986) introduced the order polytope and chain polytope of a partially ordered set and showed that they are related by a piecewise-linear homeomorphism. In this paper we vi…
Unconditional reflexive polytopes
Florian Kohl, McCabe Olsen, Raman Sanyal
A convex body is unconditional if it is symmetric with respect to reflections in all coordinate hyperplanes. In this paper, we investigate unconditional lattice polytopes with resp…
S-hypersimplices, pulling triangulations, and monotone paths
Sebastian Manecke, Raman Sanyal, Jeonghoon So
An -hypersimplex for is the convex hull of all -vectors of length with coordinate sum in . These polytopes generalize the classical hy…
Generalized angle vectors, geometric lattices, and flag-angles
Spencer Backman, Sebastian Manecke, Raman Sanyal
Interior and exterior angle vectors of polytopes capture curvature information at faces of all dimensions and can be seen as metric variants of -vectors. In this context, Gram's…
The Martin Gardner Polytopes
Kristin Fritsch, Janin Heuer, Raman Sanyal +1
In the chapter "Magic with a Matrix" in \emph{Hexaflexagons and Other Mathematical Diversions} (1988), Martin Gardner describes a delightful "party trick" to fill the squares of a…
On f- and h- vectors of relative simplicial complexes
Giulia Codenotti, Lukas Katthän, Raman Sanyal
A relative simplicial complex is a collection of sets of the form , where are simplicial complexes. Relative complexes played key roles in recent advance…
Lipschitz polytopes of posets and permutation statistics
Raman Sanyal, Christian Stump
We introduce Lipschitz functions on a finite partially ordered set and study the associated Lipschitz polytope . The geometry of can be described in terms of desce…
Minkowski complexes and convex threshold dimension
Florian Frick, Raman Sanyal
For a collection of convex bodies containing the origin, a Minkowski complex is given by those subsets whose Minkowski sum does not contain a f…
Colorful simplicial depth, Minkowski sums, and generalized Gale transforms
Karim Adiprasito, Philip Brinkmann, Arnau Padrol +3
The colorful simplicial depth of a collection of d+1 finite sets of points in Euclidean d-space is the number of choices of a point from each set such that the origin is contained…
Whitney numbers of arrangements via measure concentration of intrinsic volumes
Karim A. Adiprasito, Raman Sanyal
We verify the Rota-Heron-Welsh conjecture for matroids realizable as c-arrangements: the coefficients of the characteristic polynomial of the associated matroid are log-concave. Th…
Two double poset polytopes
Thomas Chappell, Tobias Friedl, Raman Sanyal
To every poset P, Stanley (1986) associated two polytopes, the order polytope and the chain polytope, whose geometric properties reflect the combinatorial qualities of P. This cons…
Combinatorial mixed valuations
Katharina Jochemko, Raman Sanyal
Combinatorial mixed valuations associated to translation-invariant valuations on polytopes are introduced. In contrast to the construction of mixed valuations via polarization, com…
On degree sequences of undirected, directed, and bidirected graphs
Laura Gellert, Raman Sanyal
Bidirected graphs generalize directed and undirected graphs in that edges are oriented locally at every node. The natural notion of the degree of a node that takes into account (lo…
Mixed Ehrhart polynomials
Christian Haase, Martina Juhnke-Kubitzke, Raman Sanyal +1
For lattice polytopes , Bihan (2014) introduced the discrete mixed volume in analogy to the classical mixed vo…
Combinatorial positivity of translation-invariant valuations and a discrete Hadwiger theorem
Katharina Jochemko, Raman Sanyal
We introduce the notion of combinatorial positivity of translation-invariant valuations on convex polytopes that extends the nonnegativity of Ehrhart h*-vectors. We give a surprisi…