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In combinatorial mathematics, Stanley's reciprocity theorem, named after MIT mathematician Richard P. Stanley, states that a certain functional equation is satisfied by the generating function of any rational cone (defined below) and the generating function of the cone's interior. == Definitions == A rational cone is the set of all ''d''-tuples :(''a''1, ..., ''a''''d'') of nonnegative integers satisfying a system of inequalities : where ''M'' is a matrix of integers. A ''d''-tuple satisfying the corresponding ''strict'' inequalities, i.e., with ">" rather than "≥", is in the ''interior'' of the cone. The generating function of such a cone is : The generating function ''F''int(''x''1, ..., ''x''''d'') of the interior of the cone is defined in the same way, but one sums over ''d''-tuples in the interior rather than in the whole cone. It can be shown that these are rational functions. 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「Stanley's reciprocity theorem」の詳細全文を読む スポンサード リンク
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