Une curieuse égalité entre deux sommes de produits de coefficients binomiaux
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866910165867954176 |
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| author | Mabilat, Flavien |
| author_facet | Mabilat, Flavien |
| contents | We will show in this text that, for all non-negative integers $n$ and $l$, the following equality is verified: \[\sum_{i=0}^{l} {n-i \choose i}{l+i \choose 2i+1}=\sum_{i=0}^{l} {n-i \choose i-1}{l+i \choose 2i}.\] We will first address the case where $l \leq n$, for which both sums contain only classical binomial coefficients. Then, we will consider the general framework using generalized binomial coefficients. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_23223 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Une curieuse égalité entre deux sommes de produits de coefficients binomiaux Mabilat, Flavien Combinatorics We will show in this text that, for all non-negative integers $n$ and $l$, the following equality is verified: \[\sum_{i=0}^{l} {n-i \choose i}{l+i \choose 2i+1}=\sum_{i=0}^{l} {n-i \choose i-1}{l+i \choose 2i}.\] We will first address the case where $l \leq n$, for which both sums contain only classical binomial coefficients. Then, we will consider the general framework using generalized binomial coefficients. |
| title | Une curieuse égalité entre deux sommes de produits de coefficients binomiaux |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2604.23223 |