{"title":"矩形棋盘上的皇后区独立分隔","authors":"Sowndarya Suseela Padma Kaluri, Y. Naidu","doi":"10.22342/JIMS.27.2.986.158-169","DOIUrl":null,"url":null,"abstract":"The famous eight queens problem with non-attacking queens placement on an 8 x 8 chessboard was first posed in the year 1848. The queens separation problem is the legal placement of the fewest number of pawns with the maximum number of independent queens placed on an N x N board which results in a separated board. Here a legal placement is defined as the separation of attacking queens by pawns. Using this concept, the current study extends the queens separation problem onto the rectangular board M x N, (M<N), to result in a separated board with the maximum number of independent queens. The research work here first describes the M+k queens separation with k=1 pawn and continue to find for any k. Then it focuses on finding the symmetric solutions of the M+k queens separation with k pawns.","PeriodicalId":42206,"journal":{"name":"Journal of the Indonesian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2021-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Queens Independence Separation on Rectangular Chessboards\",\"authors\":\"Sowndarya Suseela Padma Kaluri, Y. Naidu\",\"doi\":\"10.22342/JIMS.27.2.986.158-169\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The famous eight queens problem with non-attacking queens placement on an 8 x 8 chessboard was first posed in the year 1848. The queens separation problem is the legal placement of the fewest number of pawns with the maximum number of independent queens placed on an N x N board which results in a separated board. Here a legal placement is defined as the separation of attacking queens by pawns. Using this concept, the current study extends the queens separation problem onto the rectangular board M x N, (M<N), to result in a separated board with the maximum number of independent queens. The research work here first describes the M+k queens separation with k=1 pawn and continue to find for any k. Then it focuses on finding the symmetric solutions of the M+k queens separation with k pawns.\",\"PeriodicalId\":42206,\"journal\":{\"name\":\"Journal of the Indonesian Mathematical Society\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2021-07-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of the Indonesian Mathematical Society\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.22342/JIMS.27.2.986.158-169\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the Indonesian Mathematical Society","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22342/JIMS.27.2.986.158-169","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
1848年首次提出了著名的八皇后问题，即在8 x 8棋盘上放置非攻击性皇后。王后分离问题是在一块N x N的木板上合法放置数量最少的典当，而放置数量最多的独立王后，这导致了木板的分离。在这里，合法安置被定义为用棋子将攻击女王分开。利用这一概念，当前的研究将皇后区分离问题扩展到矩形板MxN，（M本文章由计算机程序翻译，如有差异，请以英文原文为准。
Queens Independence Separation on Rectangular Chessboards
The famous eight queens problem with non-attacking queens placement on an 8 x 8 chessboard was first posed in the year 1848. The queens separation problem is the legal placement of the fewest number of pawns with the maximum number of independent queens placed on an N x N board which results in a separated board. Here a legal placement is defined as the separation of attacking queens by pawns. Using this concept, the current study extends the queens separation problem onto the rectangular board M x N, (M
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