Partitions with Distinct Multiplicities of Parts: On An "Unsolved Problem" Posed By Herbert Wilf

2012/03/12 by James Allen Fill, Svante Janson, Fill, James Allen +3
Computer Science · Mathematics · #05A16 #05A17 #68W40 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #cs.DM #math.CO #msc:05A16 #msc:05A17 #msc:68W40

paper · pdf · doi:10.48550/arxiv.1203.2670

6 pages, 1 figure

arxiv created 2012/03/12 · openalex publication_date 2012/03/12 · arxiv updated 2012/03/14 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

Abstract

Wilf's Sixth Unsolved Problem asks for any interesting properties of the set of partitions of integers for which the (nonzero) multiplicities of the parts are all different. We refer to these as Wilf partitions. Using f(n) to denote the number of Wilf partitions, we establish lead-order asymptotics for lnf(n).

Related

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• Using GENERATINGFUNCTIONOLOGY to Enumerate Distinct-Multiplicity Partitions
• Combinatorial proofs for partitions with repeated smallest part
• The Number of Parts in the (Distinct) Partitions With Parts From a Set
• Asymptotics of various partitions