Identities related to integer partitions and complete Bell polynomials

• Published in: Algebra and Discrete Mathematics
• Date: 2017
• Main Authors: Mihoubi, M., Belbachir, H.
• Format: Article
• Language: English
• Published: Інститут прикладної математики і механіки НАН України 2017
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/156260
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Identities related to integer partitions and complete Bell polynomials / M. Mihoubi, H. Belbachir // Algebra and Discrete Mathematics. — 2017. — Vol. 24, № 1. — С. 158-168. — Бібліогр.: 20 назв. — англ.

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 into a given...