Arithmetic properties of 5-regular partitions into distinct parts.

A partition is said to be ℓ-regular if none of its parts is a multiple of ℓ. Let b5′(n) denote the number of 5-regular partitions into distinct parts (equivalently, into odd parts) of n. This function has also close connections to representation theory and combinatorics. In this paper, we study arithmetic properties of b5′(n). We provide full characterization of the parity of b5′(2n + 1), present several congruences modulo 4, and prove that the generating function of the sequence (b5′(5n + 1)) is lacunary modulo any arbitrary positive powers of 5. [ABSTRACT FROM AUTHOR]