Infinite families of arithmetic identities for self-conjugate 5-cores and 7-cores

DOI10.1016/j.disc.2013.12.019zbMath1351.11070OpenAlexW2085627961MaRDI QIDQ394545

Kallol Nath, Nayandeep Deka Baruah

Publication date: 27 January 2014

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.disc.2013.12.019

zbMATH Keywords

partitionstheta functions\(t\)-coresself-conjugate \(t\)-cores

Mathematics Subject Classification ID

Combinatorial aspects of partitions of integers (05A17) Partitions; congruences and congruential restrictions (11P83) Other combinatorial number theory (11B75) Analytic theory of partitions (11P82) Partition identities; identities of Rogers-Ramanujan type (11P84)

Related Items (2)

Self-conjugate partitions with the same disparity ⋮ A bijection between ordinary partitions and self-conjugate partitions with same disparity

Cites Work

• Unnamed Item
• On inequalities and linear relations for 7-core partitions
• On the representations of integers by the sextenary quadratic form \(x^2+y^2+z^2+7s^2+7t^2+7u^2\) and 7-cores
• On representations of a number as a sum of three squares
• Two congruences involving 4-cores
• Some amazing facts about \(4\)-cores
• Self-conjugate \(t\)-core partitions, sums of squares, and \(p\)-blocks of \(A_n\)
• New identities for 7-cores with prescribed BG-rank
• Cranks and t-cores
• Partition identities and Ramanujan's modular equations
• IDENTITIES FOR SELF-CONJUGATE 7- AND 9-CORE PARTITIONS
• Integer Matrix Exact Covering Systems and Product Identities for Theta Functions
• 4-core partitions and class numbers
• ELEMENTARY PROOFS OF VARIOUS FACTS ABOUT 3-CORES
• Defect zero blocks for finite simple groups
• INFINITE FAMILIES OF ARITHMETIC IDENTITIES FOR 4-CORES
• Some results on $3$-cores

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