The permuted analogues of three Catalan sets
type: Item
instance of: scholarly article
title: The permuted analogues of three Catalan sets
zbMATH Open document ID: 0777.05006
DOI: 10.1016/0378-3758(93)90035-5
published in: Journal of Statistical Planning and Inference
publication date: 1993-05-16T00:00:00Z
review text: Define the odd double factorial \(K_ n\) by \(K_ n=(2n-1)!!=(2n- 1)\cdot(2n-3)\cdot\dots\cdot 3\cdot 1\). The authors discuss three objects which are counted by the Catalan numbers but, if certain order restrictions are removed, are counted by \(K_ n\). These are sequences of paired events, complete binary trees, and arc diagrams of \(n\) chords joining \(2n\) points on a circle. The distributions of certain parameters in both kinds of sets are compared and it is found that those with the same distributions in the Catalan sets do not always have the same distributions in the permuted sets. The authors also consider the problem of extending bijections between Catalan sets to bijections between the permuted sets.
Mathematics Subject Classification ID: 05A15
zbMATH DE Number: 168229
zbMATH Keywords: odd double factorial
zbMATH Keywords: Catalan numbers
zbMATH Keywords: sequences of paired events
zbMATH Keywords: complete binary trees
zbMATH Keywords: distributions
Wikidata QID: Q55899150
author: Mark R. T. Dale
author: J. W. Moon
MaRDI profile type: Publication
full work available at URL: 0378-3758(93)90035-5
OpenAlex ID: W2021787935
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description: scientific article; zbMATH DE number 168229