Abstract
Recently, G.E. Andrews and M. Merca considered a truncated version of Euler's pentagonal number theorem and obtained a nonnegativity result. They asked the same question on a truncated Jacobi triple product identity, which can be found as a conjecture in a paper of V.J.W. Guo and J. Zeng. In this paper, we provide an answer to the question, which is purely combinatorial. We also provide a combinatorial proof of the main theorem in the paper of Andrews and Merca.
Original language | English (US) |
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Pages (from-to) | 1-14 |
Number of pages | 14 |
Journal | Journal of Combinatorial Theory. Series A |
Volume | 130 |
DOIs | |
State | Published - Feb 1 2015 |
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics