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AN ANALOGUE OF EULER’S IDENTITY AND SPLIT PERFECT PARTITIONS

  • MEGHA GOYAL (a1)

Abstract

We give the generating function of split $(n+t)$ -colour partitions and obtain an analogue of Euler’s identity for split $n$ -colour partitions. We derive a combinatorial relation between the number of restricted split $n$ -colour partitions and the function $\unicode[STIX]{x1D70E}_{k}(\unicode[STIX]{x1D707})=\sum _{d|\unicode[STIX]{x1D707}}d^{k}$ . We introduce a new class of split perfect partitions with $d(a)$ copies of each part $a$ and extend the work of Agarwal and Subbarao [‘Some properties of perfect partitions’, Indian J. Pure Appl. Math 22(9) (1991), 737–743].

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AN ANALOGUE OF EULER’S IDENTITY AND SPLIT PERFECT PARTITIONS

  • MEGHA GOYAL (a1)

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