Two Simple Ways of Generating the Partitions of (n+1) from the Partitions of n

2004/11/27 by Dhananjay P. Mehendale, Mehendale, Dhananjay P.
Mathematics · #FOS: Mathematics #General Mathematics (math.GM) #math.GM

paper · pdf · doi:10.48550/arxiv.math/0411608

7 pages

arxiv created 2004/11/27 · arxiv updated 2009/12/01

Abstract

I propose two simple ways of generating the partitions of (n+1) from the partitions of n. A recurrence relation for P(n+1), the number of partitions of (n+1), in terms of P(n) and Q(n), where Q(n) denotes the number of partitions of n having strictly different last two parts is obtained. Also a generating function for Q(n) is given. The other method for generating the partitions of (n+1) from the partitions of n is discussed at the end.

Related

• Separable Integer Partition Classes
• New partition function recurrences
• Computation of P(n,m), the Number of Integer Partitions of n into Exactly m Parts
• The Number of Parts in the (Distinct) Partitions With Parts From a Set
• Combinatorial Formula for the Partition Function