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arxiv: 1404.5404 · v1 · pith:TKJTNVPCnew · submitted 2014-04-22 · 🧮 math.NT

Congruences for the number of partitions and bipartitions with distinct even parts

classification 🧮 math.NT
keywords partscongruencesdistinctevenmodulonumberbipartitionsfamilies
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Let $ped(n)$ denote the number of partitions of $n$ wherein even parts are distinct (and odd parts are unrestricted). We show infinite families of congruences for $ped(n)$ modulo $8$. We also examine the behavior of $ped_{-2}(n)$ modulo $8$ in detail where $ped_{-2}(n)$ denotes the number of bipartitions of $n$ with even parts distinct. As a result, we find infinite families of congruences for $ped_{2}(n)$ modulo $8$.

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