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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2020
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2012.15307 |
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| _version_ | 1866916973505413120 |
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| author | Knežević, Marin Krčadinac, Vedran Relić, Lucija |
| author_facet | Knežević, Marin Krčadinac, Vedran Relić, Lucija |
| contents | We study sums of the form $\sum_{k=m}^n a_{nk} b_{km}$, where $a_{nk}$ and $b_{km}$ are binomial coefficients or unsigned Stirling numbers. In a few cases they can be written in closed form. Failing that, the sums still share many common features: combinatorial interpretations, Pascal-like recurrences, inverse relations with their signed versions, and interpretations as coefficients of change between polynomial bases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2012_15307 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Matrix products of binomial coefficients and unsigned Stirling numbers Knežević, Marin Krčadinac, Vedran Relić, Lucija Combinatorics 05A10 We study sums of the form $\sum_{k=m}^n a_{nk} b_{km}$, where $a_{nk}$ and $b_{km}$ are binomial coefficients or unsigned Stirling numbers. In a few cases they can be written in closed form. Failing that, the sums still share many common features: combinatorial interpretations, Pascal-like recurrences, inverse relations with their signed versions, and interpretations as coefficients of change between polynomial bases. |
| title | Matrix products of binomial coefficients and unsigned Stirling numbers |
| topic | Combinatorics 05A10 |
| url | https://arxiv.org/abs/2012.15307 |