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arXiv · 2406.04502

On the enumeration of series-parallel matroids

Nicholas Proudfoot·Yuan Xu·Ben Young
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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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Nicholas Proudfoot, Yuan Xu, Ben Young. 2024-10-17. On the enumeration of series-parallel matroids. https://arxiv.org/abs/2406.04502

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