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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 Bratteli–Vershik diagram ： ウィキペディア英語版 Bratteli–Vershik diagram In mathematics, a Bratteli–Veršik diagram is an ordered, essentially simple Bratteli diagram (''V'', ''E'') with a homeomorphism on the set of all infinite paths called the Veršhik transformation. It is named after Ola Bratteli and Anatoly Vershik. == Definition == Let ''X'' =  be the set of all paths in (''V'', ''E''). Let ''E''min be the set of all minimal edges in ''E'', similarly let ''E''max be the set of all maximal edges. Let ''y'' be the unique infinite path in ''E''max. The Veršhik transformation is a homeomorphism φ : ''X'' → ''X'' defined such that φ(''x'') is the unique minimal path if ''x'' = ''y''. Otherwise ''x'' = (''e''1, ''e''2,...) | ''e''''i'' ∈ ''E''''i'' where at least one ''e''''i'' ∉ ''E''max. Let ''k'' be the smallest such integer. Then φ(''x'') = (''f''1, ''f''2, ..., ''f''''k''−1, ''e''''k'' + 1, ''e''''k''+1, ... ), where ''e''''k'' + 1 is the successor of ''e''''k'' in the total ordering of edges incident on ''r''(''e''''k'') and (''f''1, ''f''2, ..., ''f''''k''−1) is the unique minimal path to ''e''''k'' + 1. The Veršhik transformation allows us to construct a pointed topological system (''X'', ''φ'', ''y'') out of any given ordered, essentially simple Bratteli diagram. The reverse construction is also defined. 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「Bratteli–Vershik diagram」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.