For more information about this meeting, contact Mary Anne Raymond.

Title: | A forest formula for the antipode in incidence Hopf algebras of posets |

Seminar: | Combinatorics/Partitions Seminar |

Speaker: | Hillary Einziger, Penn State |

Abstract: |

Incidence Hopf algebras can be defined from families of posets. These Hopf algebras have been studied in various forms by Stanley, Figueroa, Rota, and many others. In this talk, I define forests of a poset and show that these forests give rise to an antipode formula for the incidence Hopf algebra with fewer terms than the usual antipode formula, which is given as a sum over chains. Both Figueroa's (2005) formula for the antipode of the Hopf algebra of a family of distributive lattices and Schmitt's (1987) formula for the antipode in the Faa di Bruno Hopf algebra can be shown to be special cases of this new formula. In addition, the Hopf algebras for which this antipode computation is cancellation-free are exactly those which Loday and Ronco (2008) showed are equivalent to pre-Lie algebras. |

### Room Reservation Information

Room Number: | MB106 |

Date: | 04 / 26 / 2011 |

Time: | 11:15am - 12:05pm |