Chapter 1: Basic Concepts: Multinomial Coefficients
We can generalize this approach and define the multinomial coefficient.
More compactly, let n denote the sum of the ks:
Generalization of Binomial Theorem
The binomial theorem gives a formula that allows powers of binomial sums to be expanded in terms of binomial coefficients:
There is an analogous expansion for powers of multinomial sums (sums of multiple terms), in terms of these multinomial coefficients:
Any multinomial coefficient can also be expressed in terms of binomial coefficients:
The Art of Computer Programmingnotes from reading Donald Knuth's Art of Computer Programming
Part of the 2017 CS Study Plan.
Volume 2: Seminumerical Algorithms
Volume 3: Sorting and Searching
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