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arXiv · 2609.31982

Minimal transitive factorizations supported on quasi-threshold graphs

Cordelia Yuqiao Li·Ricky Ini Liu
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Abstract

We study the number of minimal transitive factorizations of the identity permutation in $S_n$ into transpositions supported on a quasi-threshold graph. We show that this number is always divisible by $(2n-2)!/n!$, which is the factorization count for a star graph, as shown by Irving and Rattan. To prove this, we give a combinatorial formula for the number of such factorizations as a weighted sum over a subset of the $n^{n-2}$ factorization trees, which are edge-weighted spanning trees satisfying certain flow constraints.

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Cordelia Yuqiao Li, Ricky Ini Liu. 2026-09-25. Minimal transitive factorizations supported on quasi-threshold graphs. https://arxiv.org/abs/2609.31982

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