On a generalization of the Pentagonal Number Theorem

DOI10.5666/KMJ.2018.58.4.599zbMath1430.05008arXiv1809.00316MaRDI QIDQ5225474

Ho-Hon Leung

Publication date: 22 July 2019

Full work available at URL: https://arxiv.org/abs/1809.00316

zbMATH Keywords

Bell polynomialsinteger partitionpolygonal numberspentagonal number theoremdivisor sum

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Combinatorial identities, bijective combinatorics (05A19) Binomial coefficients; factorials; (q)-identities (11B65) Combinatorial aspects of partitions of integers (05A17) Sums of squares and representations by other particular quadratic forms (11E25) Partitions; congruences and congruential restrictions (11P83) Arithmetic functions; related numbers; inversion formulas (11A25)

Cites Work

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• Application of Faà di Bruno's formula in characterization of inverse relations
• General identities on Bell polynomials
• A summary of Euler's work on the pentagonal number theorem
• Euler's Pentagonal Number Theorem
• Another Identity for Complete Bell Polynomials based on Ramanujan's Congruences
• Surprising Connections between Partitions and Divisors
• Quantum calculus

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