engleski

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

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.

partition identity ; direct bijection ; Durfee square ; Rogers- Ramanujan identity

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