Some inequalities for k-colored partition functions

2017/09/20 by Shane Chern, Shishuo Fu, Chern, Shane +3
Mathematics · #05A17 #11P83 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1709.06735

openalex publication_date 2017/09/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Motivated by a partition inequality of Bessenrodt and Ono, we obtain analogous inequalities for k-colored partition functions p_-k(n) for all k≥2. This enables us to extend the k-colored partition function multiplicatively to a function on k-colored partitions, and characterize when it has a unique maximum. We conclude with one conjectural inequality that strengthens our results.

Related

• Restricted k-color partitions, II
• Restricted k-color partitions
• Asymptotic formulas for general colored partition functions
• On the Bessenrodt-Ono type inequality for a wide class of A-partition functions
• Polynomization of the Bessenrodt-Ono type inequalities for A-partition functions