ISSN:
1572-9303
Keywords:
t-cores
;
parity
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
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 $$\sum\limits_{n \geqslant 0} {a_{16} \left( n \right)q^n = \frac{{(q^{16} )_\infty ^{16} }} {{(q)_\infty }}} , $$ satisfy $$a_{16} (43046721n + 457371400) \equiv a_{16} (n){\text{ (mod 2)}}{\text{.}} $$
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1009879303577
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