Divisibility Properties of the 5-regular and 13-regular Partition Functions
نویسندگان
چکیده
The function bk(n) is defined as the number of partitions of n that contain no summand divisible by k. In this paper we study the 2-divisibility of b5(n) and the 2and 3-divisibility of b13(n). In particular, we give exact criteria for the parity of b5(2n) and b13(2n).
منابع مشابه
Elementary Proofs of Parity Results for 5-regular Partitions
In a recent paper, Calkin et al. [N. Calkin, N. Drake, K. James, S. Law, P. Lee, D. Penniston and J. Radder, ‘Divisibility properties of the 5-regular and 13-regular partition functions’, Integers 8 (2008), #A60] used the theory of modular forms to examine 5-regular partitions modulo 2 and 13-regular partitions modulo 2 and 3; they obtained and conjectured various results. In this note, we use ...
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