For more information about this meeting, contact James Sellers, Stephanie Zerby, Matthew Katz, George Andrews.

Title: | Congruences for Fishburn Numbers |

Seminar: | Combinatorics/Partitions Seminar |

Speaker: | James Sellers, Penn State University |

Abstract: |

The Fishburn numbers, originally considered by Peter C. Fishburn, have been shown to enumerate a variety of combinatorial objects. These include unlabelled interval orders on n elements, (2+2)--avoiding posets with n elements, upper triangular matrices with nonnegative integer entries and without zero rows or columns such that the sum of all entries equals n, non--neighbor--nesting matches on [2n], a certain set of permutations of [n] which serves as a natural superset of the set of 231--avoiding permutations of [n], and ascent sequences of length n. However, as far as we know, the Fishburn numbers have not been studied from an arithmetic point of view. In this talk, we prove that the Fishburn numbers satisfy infinitely many Ramanujan--like congruences modulo certain primes p (the set of which we will easily describe in the talk). This is joint work with George Andrews. |

### Room Reservation Information

Room Number: | MB106 |

Date: | 02 / 04 / 2014 |

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