Hooks and powers of parts in partitions

2001/08/29 by Roland Bacher, Bacher, Roland, Laurent Manivel +1 · 3 citations
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #math.CO #math.NT #msc:05A17

paper · pdf · doi:10.48550/arxiv.math/0108199

10 pages, 1 figure

arxiv created 2001/08/29 · arxiv updated 2009/11/30

Abstract

This paper shows that the number of hooks of length k contained in all partitions of n equals k times the number of parts of length k in all partitions of n. It contains also formulas for the moments (under uniform distribution) of k-th parts in partitions of n.

Cited by

• Quasimodularity and large genus limits of Siegel-Veech constants
• Colored partitions and the hooklength formula: partition statistic identities
• Discovering hook length formulas by expansion technique

Related

• The inequality on the number of 1-hooks, 2-hooks and 3-hooks in t-regular partitions
• Inequalities and asymptotics for hook lengths in ℓ-regular partitions and ℓ-distinct partitions
• Hook length inequalities for t-regular partitions in the t-aspect
• Inequalities and asymptotics for hook numbers in restricted partitions
• Colored partitions and the hooklength formula: partition statistic identities