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arXiv · 2508.21318

Signed counting of partition matrices

Shane Chern·Shishuo Fu
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Abstract

We prove that the signed counting (with respect to the parity of the ``$\operatorname{inv}$'' statistic) of partition matrices equals the cardinality of a subclass of inversion sequences. In the course of establishing this result, we introduce an interesting class of partition matrices called improper partition matrices. We further show that a subset of improper partition matrices is equinumerous with the set of Motzkin paths. Such an equidistribution is established both analytically and bijectively.

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Shane Chern, Shishuo Fu. 2026-04-23. Signed counting of partition matrices. https://arxiv.org/abs/2508.21318

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