On the enumeration of series-parallel matroids
Nicholas Proudfoot, Yuan Xu, Ben Young
TL;DR
This paper derives explicit formulas for counting series-parallel matroids and simple series-parallel matroids based on their rank and size, extending previous combinatorial interpretations related to Kazhdan-Lusztig and Z-polynomials.
Contribution
It provides new explicit enumeration formulas for series-parallel matroids and simple series-parallel matroids, expanding on prior combinatorial interpretations.
Findings
Formulas for counting series-parallel matroids of given rank and size
Formulas for counting simple series-parallel matroids of given rank and size
Extension of previous results by Ferroni-Larson and Gao-Proudfoot-Yang-Zhang
Abstract
By the work of Ferroni and Larson, Kazhdan-Lusztig polynomials and Z-polynomials of complete graphs have combinatorial interpretations in terms of quasi series-parallel matroids. We provide explicit formulas for the number of series-parallel matroids and the number of simple series-parallel matroids of a given rank and cardinality, extending results of Ferroni-Larson and Gao-Proudfoot-Yang-Zhang.
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Taxonomy
TopicsGraph Labeling and Dimension Problems · Advanced Graph Theory Research · Advanced Algebra and Logic