Arithmetic of partitions and the $q$-bracket operator

DOI10.1090/proc/13361zbMath1357.05011arXiv1601.07466OpenAlexW2963349658MaRDI QIDQ2964028

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Publication date: 22 February 2017

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

Full work available at URL: https://arxiv.org/abs/1601.07466

zbMATH Keywords

multiplicative theory of integer partitions

Mathematics Subject Classification ID

Combinatorial aspects of partitions of integers (05A17) Arithmetic functions; related numbers; inversion formulas (11A25) Partition identities; identities of Rogers-Ramanujan type (11P84)

Related Items (19)

Special classes of \(q\)-bracket operators ⋮ Jacobi’s triple product, mock theta functions, unimodal sequences and the q-bracket ⋮ Generalizations of Alladi's formula for arithmetical semigroups ⋮ Unnamed Item ⋮ A ``supernormal partition statistic ⋮ A symmetric Bloch-Okounkov theorem ⋮ On Dirichlet series attached to quasimodular forms ⋮ On a conjecture of Hanna connecting distinct part and complete partitions ⋮ The partition function \(p(n)\) in terms of the classical Möbius function ⋮ Eichler integrals of Eisenstein series as \(q\)-brackets of weighted \(t\)-hook functions on partitions ⋮ Unnamed Item ⋮ Partition Eisenstein series and semi-modular forms ⋮ A Surprising Link Between Integer Partitions and Euler’s Number e ⋮ The product of parts or "norm" of a partition ⋮ Analytic study of norms of prime partitions ⋮ The Eichler integral of \(E_2\) and \(q\)-brackets of \(t\)-hook functions ⋮ Reciprocity between partitions and compositions ⋮ A theta identity of Gauss connecting functions from additive and multiplicative number theory ⋮ Investigation of norms of overpartitions

Cites Work

• Unnamed Item
• Unnamed Item
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• Partition zeta functions
• On \(p\)-adic modular forms and the Bloch-Okounkov theorem
• On an additive arithmetic function
• The character of the infinite wedge representation
• Partitions, quasimodular forms, and the Bloch-Okounkov theorem
• MOCK THETA FUNCTIONS AND QUANTUM MODULAR FORMS
• Hecke-type double sums, Appell-Lerch sums, and mock theta functions, I
• Dyson’s crank of a partition

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