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Congruences for Overpartition Pairs with Restricted Odd Differences
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Let b-(k) (n) denote the number of overpartition pairs of n where (i) consecutive parts di?er by a multiple of k + 1 unless the larger of the two is overlined, and (ii) the smallest part is overlined unless it is divisible by k+1. We prove many in?nite families of congruences modulo powers of 2 and 3 for b-(2) (n) and congruences modulo 4 and 5 for b-(4) (n). For example, for all n ? 0 and ?,? ? 0,
b-(4)(4·34? ·52?(5n + i) + 34? ·52?)? 0 (mod 5),
where i = 3,4.
Keywords
Congruences, Overpartitions, Restricted Odd Differences.
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