تقرير
On sequences arising from randomizing subtraction games
| العنوان: | On sequences arising from randomizing subtraction games |
|---|---|
| المؤلفون: | Capitelli, Nicolas, Somma, Francisco |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Combinatorics, 91A46, 91A60, 11B83, 40A05 |
| الوصف: | 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 $S$. Comment: 10 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2405.19593 |
| رقم الأكسشن: | edsarx.2405.19593 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |