Linear inequalities concerning partitions into distinct parts

Linear inequalities involving Euler’s partition function p ( n ) have been the subject of recent studies. In this article, we consider the partition function Q ( n ) counting the partitions of n into distinct parts. Using truncated theta series, we provide four infinite families of linear inequaliti...

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Bibliographic Details
Published in:The Ramanujan journal Vol. 58; no. 2; pp. 491 - 503
Main Author: Merca, Mircea
Format: Journal Article
Language:English
Published: New York Springer US 01.06.2022
Springer Nature B.V
Subjects:
Combinatorics
Field Theory and Polynomials
Fourier Analysis
Functions of a Complex Variable
Inequalities
Linear functions
Mathematics
Mathematics and Statistics
Number Theory
Partitions (mathematics)
11P81
Partitions
11P83
Theta series
Inequalities
Recurrences
05A17
ISSN:1382-4090, 1572-9303
Online Access:Get full text
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Summary:Linear inequalities involving Euler’s partition function p ( n ) have been the subject of recent studies. In this article, we consider the partition function Q ( n ) counting the partitions of n into distinct parts. Using truncated theta series, we provide four infinite families of linear inequalities for Q ( n ) and partition theoretic interpretations for these results.
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ISSN:1382-4090
1572-9303
DOI:10.1007/s11139-021-00427-6