Postnikov-Shapiro Algebras, Graphical Matroids and their generalizations
Combinatorics
2017-03-07 v4 Commutative Algebra
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 different equivalent definitions of spanning forests and trees, which can be read independently from other parts of the paper.
Keywords
Cite
@article{arxiv.1509.08736,
title = {Postnikov-Shapiro Algebras, Graphical Matroids and their generalizations},
author = {Gleb Nenashev},
journal= {arXiv preprint arXiv:1509.08736},
year = {2017}
}