# Symmetry distribution between hook length and part length for partitions

Abstract : It is known that the two statistics on integer partitions hook length" and part length" are equidistributed over the set of all partitions of $n$. We extend this result by proving that the bivariate joint generating function by those two statistics is symmetric. Our method is based on a generating function by a triple statistic much easier to calculate.
Document type :
Journal articles

Cited literature [13 references]

https://hal.archives-ouvertes.fr/hal-00395700
Contributor : Guo-Niu Han <>
Submitted on : Tuesday, June 16, 2009 - 11:58:43 AM
Last modification on : Thursday, July 9, 2020 - 8:40:12 AM
Long-term archiving on: : Friday, June 11, 2010 - 12:49:55 AM

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p68hooktype.pdf
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• HAL Id : hal-00395700, version 1

### Citation

Christine Bessenrodt, Guo-Niu Han. Symmetry distribution between hook length and part length for partitions. Discrete Mathematics, Elsevier, 2009, 6 p. ⟨hal-00395700⟩

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