Symmetry of \(k\)-marked Durfee symbols. (English) Zbl 1235.05015
Summary: Andrews introduced the \(k\)-marked Durfee symbols in his work defining a variant of the Atkin-Garvan moments of ranks. He provided and proved many identities and congruences using analytical methods. Here, we give an equivalent description of \(k\)-marked Durfee symbols, and using it we give combinatorial proofs to two results of Andrews.
MSC:
| 05A17 | Combinatorial aspects of partitions of integers |
| 05A19 | Combinatorial identities, bijective combinatorics |
| 11P81 | Elementary theory of partitions |
References:
| [1] | Andrews G. E., The Theory of Partitions (1976) · Zbl 0371.10001 |
| [2] | DOI: 10.1007/s00222-007-0043-4 · Zbl 1214.11116 · doi:10.1007/s00222-007-0043-4 |
| [3] | DOI: 10.1215/00127094-2008-035 · Zbl 1154.11034 · doi:10.1215/00127094-2008-035 |
| [4] | Bringmann K., Int. Math. Res. Not. 2010 pp 238– |
| [5] | Dyson F. J., Eureka (Cambridge) 8 pp 10– |
| [6] | DOI: 10.1090/S0002-9947-2010-05136-0 · Zbl 1234.11135 · doi:10.1090/S0002-9947-2010-05136-0 |
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