Pascal's simplex

Pascal's simplex

In mathematics, Pascal's simplex is a version of Pascal's triangle of more than three dimensions. As the triangle and tetrahedron are used to show the binomial and trinomial coefficients respectively, so an "n"-dimensional simplex is used to show the coefficients of an expression with "n" terms. The entries in Pascal's simplex are the multinomial coefficients:

:{n choose k_1, dots, k_m} = {n! over k_1!cdots k_m!}

where k_1+cdots+k_m=n.

This is the number of ordered partitions of a set of size "n" into "m" subsets of respective sizes "k"1, ..., "k""m".


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