Linear inequalities concerning partitions into distinct parts

• 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

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...