Congruences for the Number of Cubic Partitions Derived from Modular Forms

Details Congruences for the Number of Cubic Partitions Derived from Modular Forms Congruences for the Number of Cubic Partitions Derived from Modular Forms

2009-10-07

arxiv.org/abs/0910.1263v1

Mathematics

Number Theory

15 pages

Scientific paper

We obtain congruences for the number a(n) of cubic partitions using modular forms. The notion of cubic partitions is introduced by Chan and named by Kim in connection with Ramanujan's cubic continued fractions. Chan has shown that a(n) has several analogous properties to the number p(n) of partitions, including the generating function, the continued fraction, and congruence relations. To be more specific, we show that $a(25n+22)\equiv 0 ({\rm mod} 5)$, $a(49n+15) \equiv a(49n+29) \equiv a(49n+36) \equiv a(49n+43) \equiv 0 ({\rm mod} 7)$. Furthermore, we prove that a(n) takes infinitely many even values and infinitely odd values.

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