Sequences Derived from The Symmetric Powers of $\{1,2,\ldots,k\}$
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866910535870578688 |
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| author | Huang, Po-Yi Ke, Wen-Fong |
| author_facet | Huang, Po-Yi Ke, Wen-Fong |
| contents | For a fixed integer $k$, we define a sequence $A_k=(a_k(n))_{n\geq0}$ and a corresponding sparse subsequence $S_k$ using the cardinality of the $n$-th symmetric power of the set $\{1,2,\ldots, k\}$. For $k\in\{2,\dots,8\}$, we find recursive formulas for $S_k$, and show that the values $a_{k}(0)$, $a_{k}(1)$, and $a_{k}(3)$ are sufficient for constructing $A_{k}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_07733 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Sequences Derived from The Symmetric Powers of $\{1,2,\ldots,k\}$ Huang, Po-Yi Ke, Wen-Fong Combinatorics 11B37 For a fixed integer $k$, we define a sequence $A_k=(a_k(n))_{n\geq0}$ and a corresponding sparse subsequence $S_k$ using the cardinality of the $n$-th symmetric power of the set $\{1,2,\ldots, k\}$. For $k\in\{2,\dots,8\}$, we find recursive formulas for $S_k$, and show that the values $a_{k}(0)$, $a_{k}(1)$, and $a_{k}(3)$ are sufficient for constructing $A_{k}$. |
| title | Sequences Derived from The Symmetric Powers of $\{1,2,\ldots,k\}$ |
| topic | Combinatorics 11B37 |
| url | https://arxiv.org/abs/2307.07733 |