Journal of Integer Sequences, Vol. 17 (2014), Article 14.11.4

New Identities for the Polarized Partitions and Partitions with d-Distant Parts

Ivica Martinjak and Dragutin Svrtan
Faculty of Science
University of Zagreb
Bijenička cesta 30
HR-10000 Zagreb


In this paper we present a new class of integer partition identities. The number of partitions with d-distant parts can be written as a sum of the numbers of partitions of various lengths with 1-distant parts whose even parts, if there are any, are greater than twice the number of odd parts. We also provide a direct bijection between these classes of partitions.

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(Concerned with sequences A003106 A003114 A025157.)

Received March 14 2014; revised versions received September 1 2014; October 24 2014. Published in Journal of Integer Sequences, November 7 2014.

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