2 citations · 5 across the 10 of their papers we have counts for
8 papers · 1 filter
Lower bounds on the number of envy-free divisions
Duško Jojić, Gaiane Panina, Rade Živaljević
We analyze lower bounds for the number of envy-free divisions, in the classical Woodall-Stormquist setting and in a non-classical case, when envy-freeness is combined with the equi…
Simplicial vs. cubical spheres, polyhedral products and the Nevo-Petersen conjecture
Ivan Limonchenko, Rade Živaljević
We prove that a Murai sphere is flag if and only if it is a nerve complex of a flag nestohedron and classify all the polytopes arising in this way. Our classification implies that…
Ky Fan theorem for sphere bundles
Gaiane Panina, Rade Živaljević
The classic Ky Fan theorem is a combinatorial equivalent of Borsuk-Ulam theorem. It is a generalization and extension of Tucker's lemma and, just like its predecessor, it pinpoints…
Cooperative envy-free division
Duško Jojić, Gaiane Panina, Rade Živaljević
Relying on configuration spaces and equivariant topology, we study a general "cooperative envy-free division problem". A group of players want to cut a "cake" and divide…
Bier spheres of extremal volume and generalized permutohedra
Filip D. Jevtić, Rade T. Živaljević
A Bier sphere , defined as the deleted join of a simplicial complex and its Alexander dual , is a purely combinatorial object (abstract simplicia…
A glimpse into continuous combinatorics of posets, polytopes, and matroids
Rade T. Živaljević
This is both an expository and research paper where we advocate a systematic study of continuous analogues of finite partially ordered sets, convex polytopes, oriented matroids, ar…
Signed polyomino tilings by n-in-line polyominoes and Groebner bases
Manuela Muzika Dizdarević, Marinko Timotijević, Rade T. Živaljević
Conway and Lagarias observed that a triangular region T(m) in a hexagonal lattice admits signed tiling by three-in-line polyominoes (tribones) if and only if m=9d-1 or m=9d for som…
Combinatorics of Topological Posets:\ Homotopy complementation formulas
Rade T. Živaljević
We show that the well known {\em homotopy complementation formula} of Björner and Walker admits several closely related generalizations on different classes of topological posets (…