Generalized Lambert series and Euler's pentagonal number theorem

DOI10.1007/s00009-020-01663-8zbMath1467.11087OpenAlexW3121814448MaRDI QIDQ2222883

Mircea Merca

Publication date: 27 January 2021

Published in: Mediterranean Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00009-020-01663-8

zbMATH Keywords

partitionsLambert seriespentagonal number theorem

Mathematics Subject Classification ID

Combinatorial identities, bijective combinatorics (05A19) Combinatorial aspects of partitions of integers (05A17) Elementary theory of partitions (11P81)

Related Items (3)

A further look at cubic partitions ⋮ 6-regular partitions: new combinatorial properties, congruences, and linear inequalities ⋮ A reversal of Schur's partition theorem

Uses Software

• OEIS

Cites Work

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• The truncated pentagonal number theorem
• New relations for the number of partitions with distinct even parts
• The Lambert series factorization theorem
• Combinatorial interpretations of a recent convolution for the number of divisors of a positive integer
• Three problems in combinatorial asymptotics
• New connections between functions from additive and multiplicative number theory
• Some observations on Dyson's new symmetries of partitions
• A new look on the generating function for the number of divisors
• Factorization theorems for generalized Lambert series and applications
• On the number of even parts in all partitions of \(n\) into distinct parts
• \(q\)-hypergeometric proofs of polynomial analogues of the triple product identity, Lebesgue's identity and Euler's pentagonal number theorem
• The partition function \(p(n)\) in terms of the classical Möbius function
• New recurrence relations and matrix equations for arithmetic functions generated by Lambert series
• Generating Special Arithmetic Functions by Lambert Series Factorizations
• Counting Even and Odd Partitions
• A Partition Identity Related to Stanley’s Theorem
• Some finite generalizations of Euler's pentagonal number theorem
• A Short Proof of an Identity of Euler

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