ID | 65999 |
FullText URL | |
Author |
Motegi, Yuki
Graduate School of Pure and Applied Sciences, University of Tsukuba
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Abstract | Multiple Hook Removing Game (MHRG for short) introduced in [1] is an impartial game played in terms of Young diagrams. In this paper, we give a characterization of the set of all game positions in MHRG. As an application, we prove that for t ∈ Z≥0 and m, n ∈ N such that t ≤ m ≤ n, and a Young diagram Y contained in the rectangular Young diagram Yt,n of size t × n, Y is a game position in MHRG with Ym,n the starting position if and only if Y is a game position in MHRG with Yt,n−m+t the starting position, and also that the Grundy value of Y in the former MHRG is equal to that in the latter MHRG.
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Keywords | Young diagram
hook
combinatorial game
Grundy value
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Note | Mathematics Subject Classification. Primary 91A46; Secondary 06A07.
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Published Date | 2024-01
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Publication Title |
Mathematical Journal of Okayama University
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Volume | volume66
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Issue | issue1
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Publisher | Department of Mathematics, Faculty of Science, Okayama University
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Start Page | 31
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End Page | 44
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ISSN | 0030-1566
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NCID | AA00723502
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Content Type |
Journal Article
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language |
English
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Copyright Holders | Copyright ©2024 by the Editorial Board of Mathematical Journal of Okayama University
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File Version | publisher
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Refereed |
True
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Submission Path | mjou/vol66/iss1/2
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