## Abstract

It is shown that there are (
^{2n-r-1}
_{n-r}) noncrossing partitions of an n-set together with a distinguished block of size r, and (
^{n}
_{k-1})(
^{n-r-1}
_{k-2}) of these have k blocks, generalizing a result of Bóna on partitions with one crossing. Furthermore, specializing natural q-analogues of these formulae with q equal to certain d
^{th} roots-of-unity gives the number of such objects having d-fold rotational symmetry.

Original language | English (US) |
---|---|

Pages (from-to) | 83-87 |

Number of pages | 5 |

Journal | Ars Combinatoria |

Volume | 99 |

State | Published - Apr 1 2011 |

## Keywords

- Cyclic sieving phenonomenon
- Noncrossing partition