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

  • Adrian Avalos Coastal Carolina University
  • Mark Bly Coastal Carolina University
Keywords: q-analog; inversion statistic; generating functions; multinomial identities; major index statistic; integer partitions with kinds; generalized Galois numbers

Abstract

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.

Published
2020-06-19
How to Cite
Avalos, A., & Bly, M. (2020). Sequences, q-Multinomial Identities, Generalized Galois Numbers, and Integer Partitions with Kinds. The PUMP Journal of Undergraduate Research, 3, 72-94. Retrieved from https://journals.calstate.edu/pump/article/view/2254