Signed counting of partition matrices
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918462439292928 |
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| author | Chern, Shane Fu, Shishuo |
| author_facet | Chern, Shane Fu, Shishuo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_21318 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Signed counting of partition matrices Chern, Shane Fu, Shishuo Combinatorics Discrete Mathematics 05A05, 05A15, 05A19 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. |
| title | Signed counting of partition matrices |
| topic | Combinatorics Discrete Mathematics 05A05, 05A15, 05A19 |
| url | https://arxiv.org/abs/2508.21318 |