Sequences, q-Multinomial Identities, Generalized Galois Numbers, and Integer Partitions with Kinds.
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.
Copyright (c) 2020 Adrian Avalos, Mark Bly
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