On conjugates for set partitions and integer compositions

Details On conjugates for set partitions and integer compositions On conjugates for set partitions and integer compositions

2005-08-02

arxiv.org/abs/math/0508052v3

Mathematics

Combinatorics

Improved definition of conjugate partition; noncrossing partitions considered. 7 pages

Scientific paper

There is a familiar conjugate for integer partitions: transpose the Ferrers diagram, and a conjugate for integer compositions: transpose a Ferrers-like diagram. Here we propose a conjugate for set partitions and show that it interchanges # singletons and # adjacencies. Its restriction to noncrossing partitions cropped up in a 1972 paper of Kreweras. We also exhibit an analogous pairs of statistics interchanged by the composition conjugate.

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