| 书目名称 | Orthogonal Latin Squares Based on Groups | | 编辑 | Anthony B. Evans | | 视频video | | | 概述 | Presents the first unified proof of the Hall–Paige conjecture.Discusses the actions of groups on designs derived from latin squares.Includes an extensive list of open problems on the construction and | | 丛书名称 | Developments in Mathematics | | 图书封面 |  | | 描述 | This monograph presents a unified exposition of latin squares and mutually orthogonal sets of latin squares based on groups. Its focus is on orthomorphisms and complete mappings of finite groups, while also offering a complete proof of the Hall–Paige conjecture. The use of latin squares in constructions of nets, affine planes, projective planes, and transversal designs also motivates this inquiry. .The text begins by introducing fundamental concepts, like the tests for determining whether a latin square is based on a group, as well as orthomorphisms and complete mappings. From there, it describes the existence problem for complete mappings of groups, building up to the proof of the Hall–Paige conjecture. The third part presents a comprehensive study of orthomorphism graphs of groups, while the last part provides a discussion of Cartesian projective planes, related combinatorial structures, and a list of open problems. .Expanding the author’s 1992 monograph, .Orthomorphism Graphs of Groups., this book is an essential reference tool for mathematics researchers or graduate students tackling latin square problems in combinatorics. Its presentation draws on a basic understanding of fi | | 出版日期 | Book 2018 | | 关键词 | Orthomorphism; Complete mapping; Latin square; MOLS; Difference matrix; Orthogonality; Finite group; Finite | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-319-94430-2 | | isbn_softcover | 978-3-030-06850-9 | | isbn_ebook | 978-3-319-94430-2Series ISSN 1389-2177 Series E-ISSN 2197-795X | | issn_series | 1389-2177 | | copyright | Springer International Publishing AG, part of Springer Nature 2018 |
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发表于 2025-3-21 19:40:21
