On 5-regular bipartitions with odd parts distinct
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In his work, K. Alladi [1] considered the partition function pod(n), the number of partitions of an integer n with odd parts distinct (the even parts are unrestricted). Later Hirschhorn and Sellers [8] obtained some internal congruences involving in nite families of Ramanujan-type congruences for pod(n). Let Bo(n) denote the number of 5-regular bipartitions of a positive integer n with odd parts distinct. In this paper, we establish many in nite families of congruences modulo powers of 2 for Bo(n). For example, Bo 32 34 52 +2 72 n + t7 34 52 +1 72 1 0 (mod 16); for ; ; 0 and t7 2 f28; 92; 124; 156g.
Abstract
In his work, K. Alladi [1] considered the partition function pod(n), the number of partitions of an integer n with odd parts distinct (the even parts are unrestricted). Later Hirschhorn and Sellers [8] obtained some internal congruences involving in nite families of Ramanujan-type congruences for pod(n). Let Bo(n) denote the number of 5-regular bipartitions of a positive integer n with odd parts distinct. In this paper, we establish many in nite families of congruences modulo powers of 2 for Bo(n). For example, Bo 32 34 52 +2 72 n + t7 34 52 +1 72 1 0 (mod 16); for ; ; 0 and t7 2 f28; 92; 124; 156g.
참고문헌 (19)
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