arXiv subjects

Tanja Stojadinovic

Publications and source records attributed to Tanja Stojadinovic.

3 recordsLinked to original sources

arXiv2025

Some properties of the Redei-Berge function and related combinatorial Hopf algebras

Stanley and Grinberg introduced the symmetric function associated to digraphs, called the Redei-Berge symmetric function. In [8] is shown that this symmetric function arises from a suitable structure of combinatorial Hopf algebra on digraphs. In this paper, we introduce two new combinatorial Hopf algebras of posets and permutations and define corresponding Redei-Berge functions for them. By using both theories, of symmetric functions and of combinatorial Hopf algebras, we prove many properties of the Redei-Berge function. These include some forms of deletion-contraction property, which make it similar to the chromatic symmetric function. We also find some invariants of digraphs that are detected by the Redei-Berge function.

math.CO↗

arXiv2024

The e positivity of some new classes of graphs

We introduce two classes of graphs - suns and dumbbells, both with few variations and explore their chromatic symmetric function and its $e$-positivity. We also give many connections of these two classes with other classes of connected graphs.

math.CO↗

arXiv2014

Generalized Dehn-Sommerville relations for hypergraphs

The generalized Dehn-Sommerville relations determine the odd subalgebra of the combinatorial Hopf algebra. We introduce a class of eulerian hypergraphs that satisfy the generalized Dehn-Sommerville relations for the combinatorial Hopf algebra of hypergraphs. We characterize a wide class of eulerian hypergraphs according to the combinatorics of underlying clutters. The analogous results hold for simplicial complexes by the isomorphism which is induced from the correspondence of clutters and simplicial complexes.

math.CO↗