ID | 65999 |
フルテキストURL | |
著者 |
Motegi, Yuki
Graduate School of Pure and Applied Sciences, University of Tsukuba
|
抄録 | 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.
|
キーワード | Young diagram
hook
combinatorial game
Grundy value
|
備考 | Mathematics Subject Classification. Primary 91A46; Secondary 06A07.
|
発行日 | 2024-01
|
出版物タイトル |
Mathematical Journal of Okayama University
|
巻 | 66巻
|
号 | 1号
|
出版者 | Department of Mathematics, Faculty of Science, Okayama University
|
開始ページ | 31
|
終了ページ | 44
|
ISSN | 0030-1566
|
NCID | AA00723502
|
資料タイプ |
学術雑誌論文
|
言語 |
英語
|
著作権者 | Copyright ©2024 by the Editorial Board of Mathematical Journal of Okayama University
|
論文のバージョン | publisher
|
査読 |
有り
|
Submission Path | mjou/vol66/iss1/2
|