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
Croatia
Abstract:
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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