73 citations · 326 across the 36 of their papers we have counts for
7 papers · 1 filter
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…
Reflection groups, reflection arrangements, and invariant real varieties
Tobias Friedl, Cordian Riener, Raman Sanyal
Let be a nonempty real variety that is invariant under the action of a reflection group . We conjecture that if is defined in terms of the first basic invariants of…
Extension complexity and realization spaces of hypersimplices
Francesco Grande, Arnau Padrol, Raman Sanyal
The (n,k)-hypersimplex is the convex hull of all 0/1-vectors of length n with coordinate sum k. We explicitly determine the extension complexity of all hypersimplices as well as of…