A note on the restricted partition function \(p_{\mathcal{a}}(n, k)\)

DOI10.1016/j.disc.2022.112943zbMath1489.11166arXiv2104.04341OpenAlexW4224928212WikidataQ113877024 ScholiaQ113877024MaRDI QIDQ2144490

Krystian Gajdzica

Publication date: 14 June 2022

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2104.04341

zbMATH Keywords

partitionrestricted \(m\)-ary partitiondivisibility property of restricted partition functionodd density of restricted partition functionpartition function of a finite set

Mathematics Subject Classification ID

Partitions; congruences and congruential restrictions (11P83) Elementary theory of partitions (11P81)

Uses Software

• Mathematica

Cites Work

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• Periodicities of partition functions and Stirling numbers modulo \(p\)
• Periodicities of a class of infinite integer sequences modulo M
• The distribution of the number of parts of \(m\)-ary partitions modulo \(m\)
• Distribution of the partition function modulo \(m\)
• Recurrence sequences connected with the \(m\)-ary partition function and their divisibility properties
• Congruence properties of the \(m\)-ary partition function
• A simple proof of the Churchhouse conjecture concerning binary partitions
• Characterizing the Number of <em>m</em>-ary Partitions Modulo <em>m</em>
• PARTITIONS WITH PARTS IN A FINITE SET
• Partitions with parts in a finite set
• SOME OBSERVATIONS AND SPECULATIONS ON PARTITIONS INTO d-TH POWERS
• Parity of the partition function p(n,k)
• Partitions with Parts in a Finite Set and with Parts Outside a Finite Set
• Proof of a conjecture of Ramanujan
• On \(m\)-ary partition function congruences: A fresh look at a past problem

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