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Using sequences of finite length with positive integer elements and theinversion statistic on such sequences, a collection of binomial and multinomialidentities are extended to their $q$-analog form via combinatorial proofs.Using the major index statistic on sequences, a connection between integerpartitions with kinds and finite differences of the coefficients of generalizedGalois numbers is established.

Sequences, q-Multinomial Identities, Integer Partitions with Kinds, and Generalized Galois Numbers