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Postnikov-Shapiro Algebras, Graphical Matroids and their generalizations
Stockholm University, Faculty of Science, Department of Mathematics.
(English)Manuscript (preprint) (Other academic)
Abstract [en]

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.

Keyword [en]
Tutte polynomial, graphical matroid, spanning forest
National Category
Discrete Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-154517OAI: oai:DiVA.org:su-154517DiVA, id: diva2:1194304
Available from: 2018-03-30 Created: 2018-03-30 Last updated: 2018-04-07Bibliographically approved
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