Congruences for the Fishburn numbers

George E. Andrews, James A. Sellers

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

The Fishburn numbers, ξ( n), are defined by a formal power series expansion. ∑n=0ξ(n)qn=1+ ∑n=1j=1n(1-(1-q)j). For half of the primes p, there is a non-empty set of numbers T( p) lying in [0, p-1] such that if j∈ T(p), then for all n≥ 0, ξ(pn+j)≡0(mod p).

Original languageEnglish (US)
Pages (from-to)298-310
Number of pages13
JournalJournal of Number Theory
Volume161
DOIs
StatePublished - 2016
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2014 Elsevier Inc.

Copyright:
Copyright 2016 Elsevier B.V., All rights reserved.

Keywords

  • (2+2)-Free posets
  • Ascent sequences
  • Bernoulli polynomials
  • Congruences
  • Fishburn numbers
  • Interval orders

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