Abstract
In two papers, Little and Sellers introduced an exciting new combinatorial method for proving partition identities which is not directly bijective. Instead, they consider various sets of weighted tilings of a 1 × ∞ board with squares and dominoes, and for each type of tiling they construct a generating function in two different ways, which in turn generates a q-series identity. Using this method, they recover quite a few classical q-series identities, but Euler’s Pentagonal Number Theorem is not among them. In this paper, we introduce a key parameter when constructing the generating functions of various sets of tilings which allows us to recover Euler’s Pentagonal Number Theorem along with an uncountably infinite family of generalizations.
Original language | English |
---|---|
Pages (from-to) | 613-624 |
Number of pages | 12 |
Journal | Ramanujan Journal |
Volume | 54 |
Issue number | 3 |
DOIs | |
Publication status | Published - 2021 Apr |
Bibliographical note
Publisher Copyright:© 2019, Springer Science+Business Media, LLC, part of Springer Nature.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory