Binomial Coefficients

Some articles on binomial coefficients, coefficients, coefficient, binomial coefficient:

Binomial Coefficient - Generalizations - Generalization To Multinomials
... Binomial coefficients can be generalized to multinomial coefficients ... They are defined to be the number where While the binomial coefficients represent the coefficients of (x+y)n, the multinomial coefficients represent the coefficients of the polynomial ... The case r = 2 gives binomial coefficients The combinatorial interpretation of multinomial coefficients is distribution of n distinguishable elements over r (distinguishable) containers, each containing ...
Generalizations - Identity For The Product of Binomial Coefficients
... One can express the product of binomial coefficients as a linear combination of binomial coefficients where the connection coefficients are multinomial coefficients ... In terms of labelled combinatorial objects, the connection coefficients represent the number of ways to assign m+n-k labels to a pair of labelled combinatorial objects—of ... first object, and the unglued part of the second object.) In this regard, binomial coefficients are to exponential generating series what falling ...
Examples Of Generating Functions - Worked Example A: Basics - Bivariate Generating Functions
... For instance, since is the generating function for binomial coefficients for a fixed n, one may ask for a bivariate generating function that generates the ... find the generating function in y that has these as coefficients ... function for is just, the generating function for the binomial coefficients is and the coefficient on is the binomial coefficient ...