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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.02883 |
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| _version_ | 1866908676343726080 |
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| author | Leeb, Hannes |
| author_facet | Leeb, Hannes |
| contents | In the context of generating uniform random contingency tables with pre-specified marginals, the number of (binary) matrices with given row- and column-sums is a well-studied object in the literature. We will denote this number by $N(p,q)$, where $p$ and $q$ are the vectors of row- and column-sums. The existing literature is mainly focused on computing or approximating $N(p,q)$. In this paper, we present two identities for polynomials whose coefficients depend on the $N(p,q)$ and explore some consequences. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_02883 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An identity involving counts of binary matrices Leeb, Hannes Combinatorics Probability In the context of generating uniform random contingency tables with pre-specified marginals, the number of (binary) matrices with given row- and column-sums is a well-studied object in the literature. We will denote this number by $N(p,q)$, where $p$ and $q$ are the vectors of row- and column-sums. The existing literature is mainly focused on computing or approximating $N(p,q)$. In this paper, we present two identities for polynomials whose coefficients depend on the $N(p,q)$ and explore some consequences. |
| title | An identity involving counts of binary matrices |
| topic | Combinatorics Probability |
| url | https://arxiv.org/abs/2511.02883 |