UNIMODALITY OF k-REGULAR PARTITIONS INTO DISTINCT PARTS WITH BOUNDED LARGEST PART
Abstract
A k-regular partition into distinct parts is a partition into distinct parts with no part divisible by k. We provide a general method to establish the unimodality of k-regular partitions into distinct parts where the largest part is at most km+k−1. Let dk,m(n) denote the number of k-regular partitions of n into distinct parts where the largest part is at most km+k−1. In line with this method, we show that d4,m(n)≥d4,m(n−1) for m≥0, 1≤n≤3(m+1)2 and n≠4, and d8,m(n)≥d8,m(n−1) for m≥2 and 1≤n≤14(m+1)2. When 5≤k≤10 and k≠8, we show that dk,m(n)≥dk,m(n−1) for m≥0 and 1≤n≤⌊k(k−1)(m+1)24⌋.
Fields of Study & Subjects
Advanced Mathematical Identities
Advanced Combinatorial Mathematics
Analytic Number Theory Research
Publication details
- Journal / source
- Rocky Mountain Journal of Mathematics
- Volume
- 56
- Issue
- 1
- Pages
- 107–122
- Publication date
- 1 February 2026
- Language
- EN