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

Authors

  • Adrian Avalos Coastal Carolina University
  • Mark Bly Coastal Carolina University

DOI:

https://doi.org/10.46787/pump.v3i0.2254

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.

Downloads

Published

2020-06-19

How to Cite

Avalos, A., & Bly, M. (2020). Sequences, q-multinomial Identities, Integer Partitions with Kinds, and Generalized Galois Numbers. The PUMP Journal of Undergraduate Research, 3, 72–94. https://doi.org/10.46787/pump.v3i0.2254