On sequences arising from randomizing subtraction games
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929365927854080 |
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| author | Capitelli, Nicolas Somma, Francisco |
| author_facet | Capitelli, Nicolas Somma, Francisco |
| contents | In this article, we study the behavior of a broad family of real sequences derived from randomized one-pile subtraction games. For any subtraction set $S$, we allow any valid number of chips $s\in S$ to be removed at equal probability at any given position and we study the sequences $(a_n^S)_{n\in\mathbb{N}}$ representing the probability of winning the game from a position with $n$ chips. We characterize these sequences in terms of linear recurrence relations and examine their behavior as $n\rightarrow\infty$ for all finite $S$. We fully solve the cases for subtraction sets of fewer than 3 elements and partially complete the general case for arbitrary $S$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_19593 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On sequences arising from randomizing subtraction games Capitelli, Nicolas Somma, Francisco Combinatorics 91A46, 91A60, 11B83, 40A05 In this article, we study the behavior of a broad family of real sequences derived from randomized one-pile subtraction games. For any subtraction set $S$, we allow any valid number of chips $s\in S$ to be removed at equal probability at any given position and we study the sequences $(a_n^S)_{n\in\mathbb{N}}$ representing the probability of winning the game from a position with $n$ chips. We characterize these sequences in terms of linear recurrence relations and examine their behavior as $n\rightarrow\infty$ for all finite $S$. We fully solve the cases for subtraction sets of fewer than 3 elements and partially complete the general case for arbitrary $S$. |
| title | On sequences arising from randomizing subtraction games |
| topic | Combinatorics 91A46, 91A60, 11B83, 40A05 |
| url | https://arxiv.org/abs/2405.19593 |