On conjugates for set partitions and integer compositions
Combinatorics
2007-05-23 v3
Abstract
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.
Keywords
Cite
@article{arxiv.math/0508052,
title = {On conjugates for set partitions and integer compositions},
author = {David Callan},
journal= {arXiv preprint arXiv:math/0508052},
year = {2007}
}
Comments
Improved definition of conjugate partition; noncrossing partitions considered. 7 pages