Exact Generating Functions For The Number Of Partitions Into Distinct Parts
INTERNATIONAL JOURNAL OF NUMBER THEORY(2018)
摘要
Let Q(n) denote the number of partitions of a non-negative integer into distinct (or, odd) parts. We find exact generating functions for Q(5n + 1), Q(25n + 1) and Q(125n + 26). We deduce some congruences modulo 5 and 25. We employ Ramanujan's theta function identities and some identities for the Rogers-Ramanujan continued fraction.
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关键词
Partitions, partitions into distinct (or,odd) parts, partition congruences
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