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From a Rogers’s identity to overpartitions

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Abstract

In this paper, the author provides an efficient linear recurrence relation for the number of partitions of n into parts not congruent to 0, \(\pm 1\), \(\pm 8\), \(\pm 9\) and \(10 \pmod {20}\). A simple criterion for deciding whether this number is odd or even is given as a corollary of this result. Some results involving overpartitions and partitions into distinct parts have been derived in this context.

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Authors and Affiliations

  1. Department of Mathematics, University of Craiova, 200585, Craiova, DJ, Romania

    Mircea Merca

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  1. Mircea Merca
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Correspondence to Mircea Merca.

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Merca, M. From a Rogers’s identity to overpartitions. Period Math Hung 75, 172–179 (2017). https://doi.org/10.1007/s10998-016-0180-x

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  • DOI: https://doi.org/10.1007/s10998-016-0180-x

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