Congruences and relations for r-Fishburn numbers

2014/06/21 by Frank Garvan, Garvan, Frank
Mathematics · #05A19 #11B65 #11P83 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #math.CO #math.NT #msc:05A19 #msc:11B65 #msc:11P83

paper · pdf · doi:10.48550/arxiv.1406.5611

15 pages

arxiv created 2014/06/21 · openalex publication_date 2014/06/21 · arxiv updated 2014/06/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Recently Andrews and Sellers proved some amazing congruences for the Fishburn numbers. We extend their results to a more general sequence of numbers. As a result we prove a new congruence mod 23 for the Fishburn numbers and prove their conjectured mod 5 congruence for a related sequence. We also extend and prove some unpublished conjectures of Garthwaite and Rhoades.

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