تقرير
Maximum Nim and Josephus Problem algorithm
| العنوان: | Maximum Nim and Josephus Problem algorithm |
|---|---|
| المؤلفون: | Takahashi, Shoei, Manabe, Hikaru, Miyadera, Ryohei |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Combinatorics, 91A46, 91A05 |
| الوصف: | In this study, we study a Josephus problem algorithm. Let $n,k$ be positive integers and $g_k(n) = \left\lfloor \frac{n}{k-1} \right\rfloor +1$, where $ \left\lfloor \ \ \right\rfloor$ is a floor function. Suppose that there exists $p$ such that $g_{k}^{p-1}(0) < n(k-1) \leq g_{k}^{p}(0)$, where $g_{k}^p$ is the $p$-th functional power of $g_k$. Then, the last number that remains is $nk-h2_{k}^{p}(0)$ in the Josephus problem of $n$ numbers, where every $k$-th numbers are removed. This algorithm is based on Maximum Nim with the rule function $f_k(n)=\left\lfloor \frac{n}{k} \right\rfloor$. Using the present article's result, we can build a new algorithm for Josephus problem. Comment: arXiv admin note: substantial text overlap with arXiv:2403.19308 |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2404.06112 |
| رقم الأكسشن: | edsarx.2404.06112 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |