An explicit form of the polynomial part of a restricted partition function

DOI10.1007/s40993-016-0065-3zbMath1392.11080OpenAlexW2582836336WikidataQ94476171 ScholiaQ94476171MaRDI QIDQ515992

Christophe Vignat, Karl Dilcher

Publication date: 17 March 2017

Published in: Research in Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40993-016-0065-3

zbMATH Keywords

Bernoulli polynomialsRaabe's identityrestricted partitionsSylvester waves

Mathematics Subject Classification ID

Bernoulli and Euler numbers and polynomials (11B68) Elementary theory of partitions (11P81)

Related Items (5)

Partitions and Sylvester waves ⋮ On the restricted partition function ⋮ Log-concavity of the restricted partition function \(p_{\mathcal{A}}(n, k)\) and the new Bessenrodt-Ono type inequality ⋮ On the number of \(k\)-compositions \(n\) satisfying certain coprimality conditions ⋮ An algebraic approach to \(q\)-partial fractions and Sylvester denumerants

Uses Software

• DLMF
• PARTITIONS

Cites Work

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• Formulæ for the number of partitions of \(n\) into at most \(m\) parts (using the quasi-polynomial ansatz)
• Über Partitionen
• Partitions into \(k\) parts
• Restricted partition functions as Bernoulli and Eulerian polynomials of higher order
• General convolution identities for Bernoulli and Euler polynomials
• Sylvester waves in the Coxeter groups
• On the partial fraction decomposition of the restricted partition generating function
• Expression for restricted partition function through Bernoulli polynomials
• Applications of the classical umbral calculus
• Relations for Bernoulli–Barnes numbers and Barnes zeta functions
• The Classical Umbral Calculus
• Computing the Continuous Discretely
• The polynomial part of a restricted partition function related to the Frobenius problem

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