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Postnikov-Shapiro Algebras, Graphical Matroids and their generalizations

2015/09/29 by Nenashev, Gleb
#Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1509.08736

Abstract

In this paper we consider the original and different generalizations of Postnikov-Shapiro algebra which enumerate forests and trees of graphs, see~\citePSh. 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.

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