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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 Monk's formula ： ウィキペディア英語版 Monk's formula In mathematics, Monk's formula, found by , is an analogue of Pieri's formula that describes the product of a linear Schubert polynomial by a Schubert polynomial. Equivalently, it describes the product of a special Schubert cycle by a Schubert cycle in the cohomology of a flag manifold. Write ''t''ij for the transposition ''(i j)'', and ''s''i = ''t''i,i+1. Then 𝔖sr = ''x''1 + ⋯ + ''x''r, and Monk's formula states that for a permutation ''w'', $$ \mathfrak_ \mathfrak_w = \sum_ \mathfrak_{wt_{ij}}, where $\backslash ell(w)$ is the length of ''w''. The pairs (''i'', ''j'') appearing in the sum are exactly those such that ''i'' ≤ ''r'' < ''j'', ''w''i < ''w''j, and there is no ''i'' < ''k'' < ''j'' with ''w''i < ''w''k < ''w''j; each ''wt''ij is a cover of ''w'' in Bruhat order. ==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「Monk's formula」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.