Abstract

This entry defines the q-analogues of various combinatorial symbols, namely: the q-bracket, the q-factorial, the q-binomial coefficients, the infinite q-Pochhammer symbol, Euler’s phi function, and the finite q-Pochhammer symbol.

Proofs for many basic properties are provided, notably for the q-binomial theorem. Additionally, two identities of Euler are formalised that give power series expansions for the infinite q-Pochhammer symbol and its reciprocal.

BibTeX

@article{Combinatorial_Q_Analogues-AFP,
  author  = {Manuel Eberl},
  title   = {Combinatorial $q$-Analogues},
  journal = {Archive of Formal Proofs},
  month   = {December},
  year    = {2024},
  note    = {\url{https://isa-afp.org/entries/Combinatorial_Q_Analogues.html},
             Formal proof development},
  ISSN    = {2150-914x},
}