Sequences, q-Multinomial Identities, Integer Partitions with Kinds, and Generalized Galois Numbers
Combinatorics
2020-05-18 v2
Abstract
Using sequences of finite length with positive integer elements and the inversion statistic on such sequences, a collection of binomial and multinomial identities are extended to their -analog form via combinatorial proofs. Using the major index statistic on sequences, a connection between integer partitions with kinds and finite differences of the coefficients of generalized Galois numbers is established.
Cite
@article{arxiv.1910.11286,
title = {Sequences, q-Multinomial Identities, Integer Partitions with Kinds, and Generalized Galois Numbers},
author = {Adrian Avalos and Mark Bly},
journal= {arXiv preprint arXiv:1910.11286},
year = {2020}
}