Postnikov-Shapiro Algebras, Graphical Matroids and their generalizations

Abstract

In this paper we consider the original and different generalizations of Postnikov-Shapiro algebra which enumerate forests and trees of graphs, see~\cite{PSh}. Our main result is that the algebra counting forests depends only on graphical matroid and converse. Also we generalize algebras for a hypergraph. For this, we define spanning forests and trees of a hypergraph and the corresponding "hypergraphical" matroid. We present $3$ different equivalent definitions of spanning forests and trees, which can be read independently from other parts of the paper.

References in corpus (1)

• Products of Linear Forms and Tutte Polynomials

Cited by in corpus (2)

• On $Q$-deformations of Postnikov-Shapiro algebras
• "K-theoretic" analog of Postnikov-Shapiro algebra distinguishes graphs