On (3,4)-regular bipartitions with designated summands
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Andrews, Lewis and Lovejoy defined a new class of partitions with designated sum-mands by taking ordinary partitions and tagging exactly one of each part size. Let BPD3,4(n) denote the number of bipartitions of n with designated summands in which parts are not multiples of 3 or 4. In this paper, we establish many infinite families of congruences modulo powers of 2 for BPD3,4(n). For example, for any n≥0 and α,β,γ≥0, BPD3,4(24·32α·52β+2·72γn+b1·32α·52β+1·72γ)≡0 (mod 4), where b1∈{39, 63, 87, 111}.
Abstract
Andrews, Lewis and Lovejoy defined a new class of partitions with designated sum-mands by taking ordinary partitions and tagging exactly one of each part size. Let BPD3,4(n) denote the number of bipartitions of n with designated summands in which parts are not multiples of 3 or 4. In this paper, we establish many infinite families of congruences modulo powers of 2 for BPD3,4(n). For example, for any n≥0 and α,β,γ≥0, BPD3,4(24·32α·52β+2·72γn+b1·32α·52β+1·72γ)≡0 (mod 4), where b1∈{39, 63, 87, 111}.
참고문헌 (12)
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