Identities related to integer partitions and complete Bell polynomials

• Date: 2017
• Main Authors: Mihoubi, Miloud, Belbachir, Hacène
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2017
• Subjects: complete Bell polynomials; integer partitions; \(q\)-binomial Theorem; 11P81; 05A17
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/91
• Journal Title: Algebra and Discrete Mathematics

Using the (universal) Theorem for the integer partitions and the \(q\)-binomial Theorem, we give arithmetical and combinatorial identities for the complete Bell polynomials as generating functions for the number of partitions of a given integer into \(k\) parts and the number of partitions of \(n\)...