Abstract
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).
Original language | English (US) |
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Pages (from-to) | 281-296 |
Number of pages | 16 |
Journal | Ramanujan Journal |
Volume | 3 |
Issue number | 3 |
DOIs | |
State | Published - 1999 |
Externally published | Yes |
Keywords
- Parity
- T-cores