Euler’s “De Partitio Numerorum”

DOI10.1090/S0273-0979-07-01180-9zbMath1172.11031OpenAlexW2008162006WikidataQ56428643 ScholiaQ56428643MaRDI QIDQ5446660

George E. Andrews

Publication date: 6 March 2008

Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0273-0979-07-01180-9

zbMATH Keywords

Euler's pentagonal number theoremEuler's introduction of infinite product generating functions to the study of partitions

Mathematics Subject Classification ID

Combinatorial identities, bijective combinatorics (05A19) Combinatorial aspects of partitions of integers (05A17) Partitions; congruences and congruential restrictions (11P83) History of mathematics in the 18th century (01A50) History of number theory (11-03) Elementary theory of partitions (11P81)

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Cites Work

• Eight-vertex SOS model and generalized Rogers-Ramanujan-type identities
• Lattice gas generalization of the hard hexagon model. III: \(q\)-trinomial coefficients
• Divisibilite de certaines fonctions arithmétiques
• Automorphic forms on \(O_{s+2,2}(\mathbb R)\) and infinite products
• Distribution of the partition function modulo \(m\)
• Some continued fractions of the Rogers-Ramanujan type
• Partition identities
• The hard-hexagon model and Rogers—Ramanujan type identities
• Generalized Frobenius partitions
• Euler's Pentagonal Number Theorem
• Decomposition of the integers as a direct sum of two subsets
• ON q-DIFFERENCE EQUATIONS FOR CERTAIN WELL-POISED BASIC HYPERGEOMETRIC SERIES
• Partition Identities--From Euler to the Present
• Further Identities of the Rogers-Ramanujan Type
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