Pascal's simplex

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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 k1, ..., km.

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