The restricted partition and \(q\)-partial fractions

DOI10.1007/s40993-023-00468-4arXiv2202.03603MaRDI QIDQ6095447

N. Uday Kiran

Publication date: 8 September 2023

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

Full work available at URL: https://arxiv.org/abs/2202.03603

zbMATH Keywords

cyclotomic polynomialsRamanujan sumrestricted partitionSylvester wavesdegenerate numbers

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Bernoulli and Euler numbers and polynomials (11B68) Elementary theory of partitions (11P81) Analytic theory of partitions (11P82)

Cites Work

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• Restricted partition functions as Bernoulli and Eulerian polynomials of higher order
• The Rademacher conjecture and \(q\)-partial fractions
• Inverse cyclotomic polynomials
• Partitions and Sylvester waves
• \(h\)-adic polynomials and partial fraction decomposition of proper rational functions over \(\mathbb{R}\) or \(\mathbb{C}\)
• Ordinary and degenerate Euler numbers and polynomials
• An algebraic approach to \(q\)-partial fractions and Sylvester denumerants
• Some formulae for coefficients in restricted \(q\)-products
• Some remarks on Ramanujan sums and cyclotomic polynomials
• AN ESTIMATE FOR A RESTRICTED PARTITION FUNCTION
• Resultants of cyclotomic polynomials

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