Generalizations of Capparelli’s identity.(English)Zbl 1430.11144
The Capparelli identity states that the number of partitions of \(n\) into parts greater than \(1\) such that parts differ by at least \(2\), and at least \(4\) unless consecutive parts add up to a multiple of \(3\) is the same as the number of partitions of \(n\) into distinct parts not congruent to \(\pm 1\) modulo \(6\). One of the extensions of this identity is due to Alladi, Andrews and Gordon [K. Alladi et al., J. Algebra 174, No. 2, 636–658 (1995;Zbl 0830.05005)], in which tricolored partitions under certain difference conditions were considered. In the paper under review, the authors make use of jagged overpartitions to obtain three generalizations of the extension of Capparelli’s identity due to Alladi, Andrews and Gordon [loc. cit.]. Several corollaries of the three generalizations are also presented.
Reviewer: Shane Chern (University Park)
MSC:
| 11P84 | Partition identities; identities of Rogers-Ramanujan type |
| 05A17 | Combinatorial aspects of partitions of integers |
| 05A30 | \(q\)-calculus and related topics |
Keywords:
partition identity;Capparelli’s identity;overpartition;jagged overpartition;difference condition;generating functionCitations:
Zbl 0830.05005Cite
Online Encyclopedia of Integer Sequences:
Expansion of q-series 1 / (q^2, q^3, q^9, q^10; q^12)_infinity.References:
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