5 papers
Stability of political structures modeled by simplicial complexes under mediation, splitting, and shellability
DuÅ¡ko JojiÄ, Franjo Å arÄeviÄ
Modeling political structures by simplicial complexes, we investigate whether introducing a mediator into a substructure increases or decreases the stability of the overall structu…
Shelling of links and star clusters in edgewise subdivision of a simplex
DuÅ¡ko JojiÄ, Ognjen Papaz
We show that the combinatorial types of the links of the vertices in the edgewise triangulation of a -simplex are encoded by the partitions of . Each of these c…
A labeling of the Simplex-Lattice Hypergraph with at most 2 colors on each hyperedge
Ognjen Papaz, DuÅ¡ko JojiÄ
This paper provides a positive answer to the question of Mirzakhani and Vondrak that asks if there is a Sperner-admissible labeling of the simplex-lattice hypergraph such that each…
Sperner's colorings of hypergraphs arising from edgewise triangulations
DuÅ¡ko JojiÄ, Ognjen Papaz
We investigate Sperner's labelings of , the hypergraph whose hyperedges are facets of the edgewise triangulation of a -simplex defined by a permutation $Ï\in \m…
Lower bounds on the number of envy-free divisions
DuÅ¡ko JojiÄ, Gaiane Panina, Rade ŽivaljeviÄ
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…