Humps for Dyck and for Motzkin paths

2010/02/24 by A. Regev, Regev, A.
Mathematics · #05C30 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05C30

paper · pdf · doi:10.48550/arxiv.1002.4504

arxiv created 2010/02/24 · arxiv updated 2010/02/26

Abstract

We calculate the total number of humps in Dyck and in Motzkin paths, and we give Standard-Young-Tableaux-interpretations of the numbers involved. One then observes the intriguing phenomena that the humps-calculations change the partitions in a strip to partitions in a hook.

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