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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Higher spin alternating sign matrix ： ウィキペディア英語版 Higher spin alternating sign matrix In mathematics, a higher spin alternating sign matrix is a generalisation of the alternating sign matrix (ASM), where the columns and rows sum to an integer ''r'' (the ''spin'') rather than simply summing to 1 as in the usual alternating sign matrix definition. HSASMs are square matrices whose elements may be integers in the range −''r'' to +''r''. When traversing any row or column of an ASM or HSASM, the partial sum of its entries must always be non-negative.〔(R. E. Behrend and V. A. Knight, "Higher Spin Alternating Sign Matrices", ""The Electronic Journal of Combinatorics"", 14 (2007), #R83 )〕 High spin ASMs have found application in statistical mechanics and physics, where they have been found to represent symmetry groups in ice crystal formation. Some typical examples of HSASMs are shown below: :$$ \begin 0 & 0 & 2 & 0 \\ 0 & 2 &-1 & 1 \\ 2 &-1 & 2 &-1 \\ 0 & 1 &-1 & 2 \end;\quad \begin 0 & 0 & 2 & 0&0 \\ 0 & 1 &-1 & 2 &0\\ 2 &-1 &-1 & 0 &2\\ 0 & 0 & 2 & 0 &0\\ 0&2&0&0&0 \end;\quad \begin 0 & 0 & 0 & 2 \\ 0 & 2 & 0 & 0 \\ 2 &-2 & 2 & 0 \\ 0 & 2 & 0 & 0 \end;\quad \begin 0 & 2 & 0 & 0 \\ 0 & 0 & 0 & 2 \\ 2 & 0 & 0 & 0 \\ 0 & 0 & 2 & 0 \end. The set of HSASMs is a superset of the ASMs. The extreme points of the convex hull of the set of ''r''-spin HSASMs are themselves integer multiples of the usual ASMs. ==References== 〔 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Higher spin alternating sign matrix」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.