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Pascal's simplex : ウィキペディア英語版
Pascal's simplex
In mathematics, Pascal's simplex is a generalisation of Pascal's triangle into arbitrary number of dimensions, based on the multinomial theorem.
== Generic Pascal's ''m''-simplex ==
Let ''m'' (''m'' > 0) be a number of terms of a polynomial and ''n'' (''n'' ≥ 0) be a power the polynomial is raised to.
Let \wedge^m denote a Pascal's ''m''-simplex. Each Pascal's ''m''-simplex is a semi-infinite object, which consists of an infinite series of its components.
Let \wedge^m_n denote its ''n''th component, itself a finite (''m − 1'')-simplex with the edge length ''n'', with a notational equivalent \vartriangle^_n.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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