A note on the restricted partition function p_A(n,k)

2021/04/09 by Krystian Gajdzica, Gajdzica, Krystian · 2 citations
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2104.04341

openalex publication_date 2021/04/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let A=(a_n)_n∈ℕ+ be a sequence of positive integers. Let p_A(n,k) denote the number of multi-color partitions of n into parts in \a₁,…,a_k\. We examine several arithmetic properties of the sequence (p_A(n,k) \pmodm)_n∈ℕ for an arbitrary fixed integer m\geqslant2. We investigate periodicity of the sequence and lower and upper bounds for the density of the set \n∈ℕ: p_A(n,k) ≡ i \pmodm\ for a fixed positive integer k and i∈\0,1,…, m-1\. In particular, we apply our results to the special cases of the sequence A. Furthermore, we present some results related to restricted m-ary partitions.

Cited by

• Rectangle partitions generalizing integer partitions
• Special restricted partition functions for the stable sheaf cohomology on flag varieties

Related

• Restricted integer partition functions
• Parity of the Partition Function p(n,k)
• Partitions into prime powers
• Restricted k-color partitions, II
• Polynomization of the Bessenrodt-Ono type inequalities for A-partition functions