33 citations · 88 across the 15 of their papers we have counts for
8 papers · 1 filter
Cone and constrained colorful Carathéodory Theorems
Pavle V. M. Blagojević, Roman N. Karasev, Bálint Zsigri
Holmsen proved in 2016 a generalization of the classical colorful Caratheodory theorem in which a matroid imposes additional constraints on the desired colorful transversal. His ap…
Cutting a part from many measures
Pavle V. M. Blagojević, Nevena Palić, Pablo Soberón +1
Holmsen, Kynčl and Valculescu recently conjectured that if a finite set with points in that is colored by different colors can be partitioned into $…
Beyond the Borsuk-Ulam theorem: The topological Tverberg story
Pavle V. M. Blagojević, Günter M. Ziegler
Bárány's "topological Tverberg conjecture" from 1976 states that any continuous map of an -simplex to , for , maps points from disjoint f…
The topological transversal Tverberg theorem plus constraints
Pavle V. M. Blagojević, Aleksandra S. Dimitrijević Blagojević, Günter M. Ziegler
In this paper we use the strength of the constraint method in combination with a generalized Borsuk-Ulam type theorem and a cohomological intersection lemma to show how one can obt…
Barycenters of Polytope Skeleta and Counterexamples to the Topological Tverberg Conjecture, via Constraints
Pavle V. M. Blagojević, Florian Frick, Günter M. Ziegler
Using the authors' 2014 "constraints method," we give a short proof for a 2015 result of Dobbins on representations of a point in a polytope as the barycenter of points in a skelet…
Tverberg plus constraints
Pavle V. M. Blagojević, Florian Frick, Günter M. Ziegler
Many of the strengthenings and extensions of the topological Tverberg theorem can be derived with surprising ease directly from the original theorem: For this we introduce a proof…
A tight colored Tverberg theorem for maps to manifolds
Pavle V. M. Blagojević, Benjamin Matschke, Günter M. Ziegler
We prove that any continuous map of an N-dimensional simplex Delta_N with colored vertices to a d-dimensional manifold M must map r points from disjoint rainbow faces of Delta_N to…
Optimal bounds for the colored Tverberg problem
Pavle V. M. Blagojević, Benjamin Matschke, Günter M. Ziegler
We prove a "Tverberg type" multiple intersection theorem. It strengthens the prime case of the original Tverberg theorem from 1966, as well as the topological Tverberg theorem of B…