Inequalities for full rank differences of 2-marked Durfee symbols

DOI10.1016/j.jcta.2011.10.003zbMath1232.05015arXiv1102.1814OpenAlexW1985820836MaRDI QIDQ654903

Kathrin Bringmann, Ben Kane

Publication date: 23 December 2011

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1102.1814

zbMATH Keywords

partitionscongruencesrankRamanujan\(k\)-marked Durfee symbols

Mathematics Subject Classification ID

Combinatorial identities, bijective combinatorics (05A19) Combinatorial aspects of partitions of integers (05A17)

Cites Work

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• Partitions, Durfee symbols, and the Atkin-Garvan moments of ranks
• Dyson's ranks and Maass forms
• The generating functions of the rank and crank modulo 8
• Distribution of the full rank in residue classes for odd moduli
• Relations between the ranks and cranks of partitions
• The ranks and cranks of partitions moduli 2, 3, and 4
• On two geometric theta lifts
• Distribution of the partition function modulo \(m\)
• The nonholomorphic parts of certain weak Maass forms
• Inequalities for differences of Dyson's rank for all odd moduli
• Eulerian series as modular forms
• Rank generating functions as weakly holomorphic modular forms
• Asymptotics for rank partition functions
• CONGRUENCES FOR DYSON'S RANKS
• New Combinatorial Interpretations of Ramanujan's Partition Congruences Mod 5,7 and 11
• Dyson’s crank of a partition
• Congruence properties for the partition function
• Partition Statistics and Quasiharmonic Maass Forms
• Some Properties of Partitions

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