6 citations · 34 across the 28 of their papers we have counts for
25 papers · 1 filter
Polytopality of simple games
Marinko Timotijević, Rade T. Živaljević, Filip D. Jevtić
The Bier sphere and the canonical fan are combinatorial/geometric companions of a simple game …
Colored Tverberg Theorems for non-prime powers
Leandro V. Mauri, Rade T. Živaljević, Denise de Mattos +1
We prove a relative of the Optimal (Type B)} Colored Tverberg theorem of Živaljević and Vrećica which modifies this results in two different ways. (1) Our result is valid if the nu…
Envy-free division in the presence of a dragon
Gaiane Panina, Rade Živaljević
We prove several results addressing the envy-free division problem in the presence of an unpredictable (secretive) player, called the "dragon". There are two basic scenarios. 1. Th…
Envy-free division via configuration spaces
Gaiane Panina, Rade Živaljević
The classical approach to envy-free division and equilibrium problems relies on Knaster-Kuratowski-Mazurkiewicz theorem, Sperner's lemma or some extension involving mapping degree.…
Splitting necklaces, with constraints
Duško Jojić, Gaiane Panina, Rade Živaljević
We prove several versions of N. Alon's "necklace-splitting theorem", subject to additional constraints, as illustrated by the following results. (1) The "almost equicardinal neckla…
A Tverberg type theorem for collectively unavoidable complexes
Duško Jojić, Gaiane Panina, Rade Živaljević
We prove (Theorem 2.4) that the symmetrized deleted join of a "balanced family" of collectively -unavoidabl…
Cyclohedron and Kantorovich-Rubinstein polytopes
Filip D. Jevtić, Marija Jelić, Rade T. Živaljević
We show that the cyclohedron (Bott-Taubes polytope) arises as the dual of a Kantorovich-Rubinstein polytope , where is a quasi-metric (asymmetric distance function…
Symmetric multiple chessboard complexes and a new theorem of Tverberg type
Duško Jojić, Siniša Vrećica, Rade Živaljević
We prove a new theorem of Tverberg type which confirms the conjecture of Blagojevic, Frick, and Ziegler about the existence of "balanced Tverberg partitions" (Conjecture 6.6 in, Tv…
Multiple chessboard complexes and the colored Tverberg problem
Duško Jojić, Siniša T. Vrećica, Rade T. Živaljević
Following D.B. Karaguezian, V. Reiner, and M.L. Wachs (Matching Complexes, Bounded Degree Graph Complexes, and Weight Spaces of -Complexes, Journal of Algebra 2001) we study th…
Symmetric polyomino tilings, tribones, ideals, and Groebner bases
Manuela Muzika Dizdarevic, Rade T. Zivaljevic
We apply the theory of Groebner bases to the study of signed, symmetric polyomino tilings of planar domains. Complementing the results of Conway and Lagarias we show that the trian…
Measurable patterns, necklaces, and sets indiscernible by measure
Sinisa Vrecica, Rade Zivaljevic
In some recent papers the classical `splitting necklace theorem' is linked in an interesting way with a geometric `pattern avoidance problem'. We explore the topological constraint…
Chessboard complexes indomitable
S. T. Vrecica, R. T. Zivaljevic
We give an alternative proof of the striking new Tverberg type theorem of Blagojevic and Ziegler, arXiv:0910.4987v1 [math.CO]. Our method also yields some new cases of "constrained…
Fulton-MacPherson compactification, cyclohedra, and the polygonal pegs problem
Sinisa Vrecica, Rade Zivaljevic
The cyclohedron (Bott-Taubes polytope) arises both as the polyhedral realization of the poset of all cyclic bracketings of a circular word and as an essential part of the Fulton-Ma…
Oriented matroids and Ky Fan's theorem
Rade T. Zivaljevic
L. Lovasz has shown that Sperner's combinatorial lemma admits a generalization involving a matroid defined on the set of vertices of the associated triangulation. Inspired by this…
Splitting multidimensional necklaces
Mark de Longueville, Rade Zivaljevic
The well-known "splitting necklace theorem" of Noga Alon says that each "necklace" having beads of n different colors can be fairly divided between k "thieves" by at most n(k-1) cu…
Groupoids in combinatorics -- applications of a theory of local symmetries
Rade T. Zivaljevic
An objective of the theory of combinatorial groupoids is to introduce concepts like "holonomy", "parallel transport", "bundles", "combinatorial curvature" etc. in the context of si…
Combinatorial groupoids, cubical complexes, and the Lovasz conjecture
Rade T. Zivaljevic
A foundation is laid for a theory of combinatorial groupoids, allowing us to use concepts like ``holonomy'', ``parallel transport'', ``bundles'', ``combinatorial curvature'' etc. i…
The Borsuk-Ulam-property, Tucker-property and constructive proofs in combinatorics
Mark de Longueville, Rade T. Zivaljevic
This article is concerned with a general scheme on how to obtain constructive proofs for combinatorial theorems that have topological proofs so far. To this end the combinatorial c…
Parallel transport of -complexes and the Lovasz conjecture
Rade T. Zivaljevic
The groupoid of projectivities, introduced by M. Joswig, serves as a basis for a construction of parallel transport of graph and more general -complexes. In this framework we…
Equipartitions of measures in
Rade T. Zivaljevic
We prove that each measure in admits an equipartition by 4 hyperplanes, provided that it is symmetric with respect to a 2-dimensional, affine subspace of . Moreo…
WI-posets, graph complexes and Z_2-equivalences
Rade T. Zivaljevic
We introduce WI-posets as intermediate objects in the study of Z_2-homotopy types of graph complexes. It turns out that (almost) all graph complexes associated to a graph can be vi…
Topology and Combinatorics of Partitions of Masses by Hyperplanes
Peter Mani-Levitska, Sinisa Vrecica, Rade Zivaljevic
One of our result is that 5 measurable sets in always admit an equipartition by 2 hyperplanes. This is an instance of a general equipartition problem (formulated by B. Gr{\"…
Symmetric products of surfaces and the cycle index
Pavle Blagojevic, Vladimir Grujic, Rade Zivaljevic
We express the signature of the symmetric product of an (open) surface in terms of the cycle index of , a polynomial which or…
Arrangements of symmetric products of spaces
Pavle Blagojevic, Vladimir Grujic, Rade Zivaljevic
Using the topological technique of diagrams of spaces, we calculate the homology of the union and the complement of finite arrangements of subspaces of the form i…