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Mathematics > Combinatorics

Title: Maximum Nim and Josephus Problem

Authors: Shoei Takahashi, Hikaru Manabe, Ryohei Miyadera
(Submitted on 28 Mar 2024)
Abstract: In this study, we study the relation between Grundy numbers of a Maximum Nim and Josephus problem. Let f(x) = floor(x/k), where floor( ) is the floor function and k is a positive integer. We prove that there is a simple relation with a Maximum Nim with the rule function f and the Josephus problem in which every k-th numbers are to be removed.
Comments: This is the first result that treats the relation between general Josephus problem and the maximum nim
Subjects: Combinatorics (math.CO)
MSC classes: 91A46, 91A05
ACM classes: G.2
Cite as: arXiv:2403.19308 [math.CO]
  (or arXiv:2403.19308v1 [math.CO] for this version)

Submission history

From: Ryohei Miyadera Dr [view email]
[v1] Thu, 28 Mar 2024 10:47:30 GMT (22kb)
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