Arithmetic Properties of Overcubic Partition Pairs

Bernard L.S. Lin

Abstract


Let $\overline{b}(n)$ denote the number of overcubic partition pairs of $n$. In this paper, we establish two Ramanujan type congruences and several infinite families of congruences modulo $3$ satisfied by $\overline{b}(n)$ . For modulus $5$, we obtain one Ramanujan type congruence and two congruence relations for $\overline{b}(n)$, from which some strange congruences are derived.


Keywords


Overcubic partition pairs; Theta function; Congruence

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