On some conjectures of Aygin and Chan on inequalities of linear combinations of cranks of partitions

DOI10.1007/s13398-024-01676-yMaRDI QIDQ6660214

Wei-Feng Gao, Olivia X. M. Yao, Eric H. Liu

Publication date: 10 January 2025

Published in: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM (Search for Journal in Brave)

zbMATH Keywords

partitionsinequalitiesrankasymptotic formulasCrank

Mathematics Subject Classification ID

Combinatorial aspects of partitions of integers (05A17) Partitions; congruences and congruential restrictions (11P83) Asymptotic enumeration (05A16) Arithmetic functions; related numbers; inversion formulas (11A25) Analytic theory of partitions (11P82)

Cites Work

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• The generating functions of the rank and crank modulo 8
• On some relations between the rank and the crank
• The ranks and cranks of partitions moduli 2, 3, and 4
• On ranks and cranks of partitions modulo 4 and 8
• On a generalized crank for \(k\)-colored partitions
• Asymptotics for the Fourier coefficients of eta-quotients
• Combinations of ranks and cranks of partitions moduli 6, 9 and 12 and their comparison with the partition function
• New equalities and inequalities for the ranks and cranks of partitions
• The Crank of Partitions Mod 8, 9 and 10
• Dyson’s crank of a partition
• On the Rank and the Crank Modulo 4
• Relations Between the Rank and the Crank Modulo 9
• On the Rank and the Crank Modulo 4 and 8
• Some inequalities for Garvan's bicrank function of 2-colored partitions
• Some Properties of Partitions

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