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 language | English (US) |
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Pages (from-to) | 427-442 |
Number of pages | 16 |
Journal | Annals of Combinatorics |
Volume | 23 |
Issue number | 3-4 |
DOIs | |
State | Published - Nov 1 2019 |
Keywords
- Congruences
- Fishburn numbers
- Kontsevich–Zagier strange function
- Partial theta functions
- q-Series
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics