English

Factors of Some Lacunary q-Binomial Sums

Number Theory 2012-06-05 v3 Combinatorics

Abstract

In this paper, we prove a divisibility result for the lacunary qq-binomial sum kr(modc)(1)kq(k2)\qbinomnkq\qbinom(kr)/clqc. \sum_{k\equiv r\pmod{c}}(-1)^kq^{\binom{k}{2}}\qbinom{n}{k}{q}\qbinom{(k-r)/c}{l}{q^{c}}.

Keywords

Cite

@article{arxiv.1201.5963,
  title  = {Factors of Some Lacunary q-Binomial Sums},
  author = {Hao Pan},
  journal= {arXiv preprint arXiv:1201.5963},
  year   = {2012}
}