Sequences, q-multinomial Identities, Integer Partitions with Kinds, and Generalized Galois Numbers - Avalos, Adrian; Bly, Mark (The PUMP Journal of Undergraduate Research, 2020)
Using sequences of finite length with positive integer entries and the inversion statistic on such sequences, a collection of binomial and multinomial identities are extended to their q-analog form via combinatorial proofs. Using the major index statistic on sequences, a connection between finite differences of the coefficients of generalized Galois numbers and integer partitions with kinds is established.