Involve: A Journal of Mathematics
- Volume 4, Number 4 (2011), 411-416.
Congruence properties of $S$-partition functions
We study the function that counts the number of partitions of with elements in , where is a set of integers. Generalizing previous work of Kronholm, we find that given a positive integer , the coefficients of the generating function of are periodic modulo , and we use this periodicity to obtain families of -partition congruences. In particular, we obtain families of congruences between partition functions and .
Involve, Volume 4, Number 4 (2011), 411-416.
Received: 28 April 2011
Accepted: 17 June 2011
First available in Project Euclid: 20 December 2017
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Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 11P83: Partitions; congruences and congruential restrictions
Gruet, Andrew; Wang, Linzhi; Yu, Katherine; Zeng, Jiangang. Congruence properties of $S$-partition functions. Involve 4 (2011), no. 4, 411--416. doi:10.2140/involve.2011.4.411. https://projecteuclid.org/euclid.involve/1513733433