Connection between ordinary multinomials, generalized Fibonacci numbers, partial Bell partition polynomials and convolution powers of discrete uniform distribution

Abstract

Using an explicit computable expression of ordinary multinomials, we establish three remarkable connections, with the q-generalized Fibonacci sequence, the exponential partial Bell partition polynomials and the density of convolution powers of the discrete uniform distribution. Identities and various combinatorial relations are derived.

9 pages

References in corpus (2)

• The Andrews-Gordon identities and $q$-multinomial coefficients
• Refined q-trinomial coefficients and character identities

Cited by in corpus (4)

• A fast algorithm for computing Bell polynomials based on index break-downs using prime factorization
• Unimodality of ordinary multinomials and maximal probabilities of convolution powers of discrete uniform distribution
• Point Counts of D_k and Some A_k and E_k Integer Lattices Inside Hypercubes
• Super-congruences involving trininomial coefficients