Kolitsch and Sellers showed recently that a8(n), the number of 8-core partitions of n, is even when n belongs to certain arithmetic progressions. We prove a similar result for 16-cores. In doing so, we prove the surprising result that the a16(n), given by ∑ a16(n) qn = (q16)∞16/(q)∞, n≥0 satisfy a16(43046721n + 457371400) ≡ a16(n) (mod 2).
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory