Dissections of Strange q-Series

Scott Ahlgren, Byungchan Kim, Jeremy Lovejoy

Research output: Contribution to journalArticle

Abstract

In a study of congruences for the Fishburn numbers, Andrews and Sellers observed empirically that certain polynomials appearing in the dissections of the partial sums of the Kontsevich–Zagier series are divisible by a certain q-factorial. This was proved by the first two authors. In this paper, we extend this strong divisibility property to two generic families of q-hypergeometric series which, like the Kontsevich–Zagier series, agree asymptotically with partial theta functions.

Original languageEnglish (US)
Pages (from-to)427-442
Number of pages16
JournalAnnals of Combinatorics
Volume23
Issue number3-4
DOIs
StatePublished - Nov 1 2019

Keywords

  • Congruences
  • Fishburn numbers
  • Kontsevich–Zagier strange function
  • Partial theta functions
  • q-Series

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

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