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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2312.00301 |
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| _version_ | 1866910962298126336 |
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| author | Shunia, Joseph M. Sauras-Altuzarra, Lorenzo |
| author_facet | Shunia, Joseph M. Sauras-Altuzarra, Lorenzo |
| contents | We construct arithmetic terms representing the partial sums of binomial coefficients, and we extend these results to obtain arithmetic terms representing the multisections of binomial coefficient sums. We also introduce an arithmetic term representing a certain type of multinomial coefficient sum and, as an application, we provide an arithmetic term representing the central trinomial coefficients. This solves one of the research problems of the celebrated book Concrete Mathematics, which remained open for nearly thirty years. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_00301 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Arithmetic Terms for Multinomial Coefficient Sums Shunia, Joseph M. Sauras-Altuzarra, Lorenzo General Mathematics 11B65, 11Y55, 11A25 We construct arithmetic terms representing the partial sums of binomial coefficients, and we extend these results to obtain arithmetic terms representing the multisections of binomial coefficient sums. We also introduce an arithmetic term representing a certain type of multinomial coefficient sum and, as an application, we provide an arithmetic term representing the central trinomial coefficients. This solves one of the research problems of the celebrated book Concrete Mathematics, which remained open for nearly thirty years. |
| title | Arithmetic Terms for Multinomial Coefficient Sums |
| topic | General Mathematics 11B65, 11Y55, 11A25 |
| url | https://arxiv.org/abs/2312.00301 |