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Integer points enumerator of hypergraphic polytopes
(Mathematical Institute of the Serbian Academy of Sciences and Arts, 2021)
For a hypergraphic polytope there is a weighted quasisymmetric
function which enumerates positive integer points in its normal fan
and determines its f −polynomial. This quasisymmetric function
invariant of hypergraphs ...
Weighted P-partitions enumerator
(Applicable Analysis and Discrete Mathematics, 2021)
To an extended generalized permutohedron we associate the weighted integer points enumerator, whose principal specialization is the f-polynomial. In the case of poset cones it refines Gessel's P-partitions enumerator. We ...
Еxtended Schatten norms of random graphs and Nikiforov conjecture
(Hacettepe University, 2022)
In this paper we give a geometric mean and mean of
p-th degree of singular values for almost all graphs. We prove three
theorems about a conjecture of V. Nikiforov for Schatten p-norm
of graphs when p > 2. We prove that ...
Between graphical zonotope and graph-associahedron
(Turkish Journal of Mathematics, 2023)
This manuscript introduces a finite collection of generalized permutohedra associated to a simple graph. The first polytope of this collection is the graphical zonotope of the graph and the last is the graph–associahedron ...