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Mathematics > Combinatorics

arXiv:1804.08809 (math)
[Submitted on 24 Apr 2018 (v1), last revised 31 Dec 2019 (this version, v4)]

Title:The Sprague-Grundy Functions of Saturations of Misere Nim

Authors:Yuki Irie
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Abstract:We consider misère Nim as a normal-play game obtained from Nim by removing the terminal position. While explicit formulas are known for the Sprague-Grundy functions of Nim and Welter's game, no explicit formula is known for that of misère Nim. All three of these games can be considered as position restrictions of Nim. What are the differences between them? We point out that Nim and Welter's game are saturated, but misère Nim is not. Moreover, we present explicit formulas for the Sprague-Grundy functions of saturations of misère Nim, which are obtained from misère Nim by adjoining some moves.
Subjects: Combinatorics (math.CO)
MSC classes: 91A46
Cite as: arXiv:1804.08809 [math.CO]
  (or arXiv:1804.08809v4 [math.CO] for this version)
  https://doi.org/10.48550/arXiv.1804.08809
Journal reference: The Electronic Journal of Combinatorics 28(1), P1.58, 2021
Related DOI: https://doi.org/10.37236/8916

Submission history

From: Yuki Irie [view email]
[v1] Tue, 24 Apr 2018 02:03:26 UTC (11 KB)
[v2] Mon, 20 May 2019 07:28:57 UTC (17 KB)
[v3] Thu, 23 May 2019 07:44:15 UTC (17 KB)
[v4] Tue, 31 Dec 2019 09:44:11 UTC (18 KB)
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