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The Bressoud-Göllnitz-Gordon theorem for overpartitions of even moduli. (English) Zbl 1387.05015

Summary: We give an overpartition analogue of Bressoud’s combinatorial generalization of the Göllnitz-Gordon theorem for even moduli in general case. Let \(\widetilde{O}_{k,i}(n)\) be the number of overpartitions of \(n\) whose parts satisfy certain difference condition and \(\widetilde{P}_{k,i}(n)\) be the number of overpartitions of \(n\) whose non-overlined parts satisfy certain congruence condition. We show that \(\widetilde{O}_{k,i}(n) = \widetilde{P}_{k,i}(n)\) for \(1 \leq i < k\).

MSC:

05A17 Combinatorial aspects of partitions of integers
11P84 Partition identities; identities of Rogers-Ramanujan type
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References:

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