2 citations · 3 across the 5 of their papers we have counts for
4 papers · 1 filter
Jordan-Hölder with uniqueness for semimodular semilattices
Pavel Paták
We present a short proof of the Jordan-Hölder theorem with uniqueness for semimodular semilattice: Given two maximal chains in a semimodular semilattice of finite height, they both…
A sharper Ramsey theorem for constrained drawings
Pavel Paták
Given a graph and a collection of subsets of indexed by the subsets of vertices of , a constrained drawing of is a drawing, where each edge i…
Tverberg type theorems for matroids
Pavel Paták
In this paper we show a variant of colorful Tverberg's theorem which is valid in any matroid: Let be a sequence of non-loops in a matroid of finite rank with closure op…
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…