New infinite families of congruences for 5-core and 7-core partitions (Q6548004)
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scientific article; zbMATH DE number 7857909
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | New infinite families of congruences for 5-core and 7-core partitions |
scientific article; zbMATH DE number 7857909 |
Statements
New infinite families of congruences for 5-core and 7-core partitions (English)
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31 May 2024
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Let \(a_t(n)\) denote the number of \(t\)-core partitions of \(n\) as usual in Ramanujan mathematics. A number of congruences for \(a_t(n)\) have been discovered for some small \(t\). It has been proven some new infinite families of congruences modulo 3 for \(a_5(n)\) and congruences modulo 2 for \(a_7(n)\) by utilizing Newman's identities. The number 2, 3, 5 and 7 are considered as small numbers.
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partition
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congruence
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\(t\)-core partition
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Newman's identity
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