4-Regular partitions and the pod function

2021/11/21 by Ballantine, Cristina, Merca, Mircea
#05A19 #05A20 #11P81 #11P82 #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2111.10702

Abstract

The partition function pod(n) enumerates the partitions of n wherein odd parts are distinct and even parts are unrestricted. Recently, a number of properties for pod(n) have been established. In this paper, for k∈\0,2\ we consider the partitions of n into distinct parts not congruent to k modulo 4 and the 4-regular partitions of n in order to obtain new properties for pod(n). In this context, we derive two new infinite families of linear inequalities involving the function pod(n) and obtain new identities of Watson type.

Related

• The pod function and its connection with other partition functions
• PED and POD partitions: combinatorial proofs of recurrence relations
• Generalizations of POD and PED partitions
• Arithmetic of 2-regular partitions with distinct odd parts
• Identities involving partitions with distinct even parts and 4-regular partitions