Ognjen Papaz

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20242026

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math.CO2026

A geometric proof of the Brenti--Welker identity

Ognjen Papaz

We construct a hypersimplicial subdivision of the $r$ -dilation of the $i$ -th hypersimplex of dimension $d$ that provides a geometric proof of the Brenti--Welker identity.

math.CO2025

A labeling of the Simplex-Lattice Hypergraph with at most 2 colors on each hyperedge

Ognjen Papaz, Duško Jojić

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…

math.CO2025

Sperner's colorings of hypergraphs arising from edgewise triangulations

Duško Jojić, Ognjen Papaz

We investigate Sperner's labelings of $H_{k, q}^{π}$ , the hypergraph whose hyperedges are facets of the edgewise triangulation of a $(k - 1)$ -simplex defined by a permutation $π\in \mat…

math.CO2024

Shelling of links and star clusters in edgewise subdivision of a simplex

Duško Jojić, Ognjen Papaz

We show that the combinatorial types of the links of the vertices in the edgewise triangulation $T_{k, q}$ of a $(k - 1)$ -simplex are encoded by the partitions of $k$ . Each of these c…