## 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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