Area of Catalan paths

A Catalan path of length n, is a path from (0,0) going N=(0,1) or E=(0,1) in each step, such that it stays under (or on) the line x= y and ending at ( n, n) after 2 n steps. Here we calculate the total area between the line y= x and all Catalan paths. The total area a n= 1 2 ∑ k=1 nc k4 n−k , where...

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Bibliographic Details
Published inDiscrete mathematics Vol. 226; no. 1; pp. 439 - 444
Main Author Woan, Wen-jin
Format Journal Article
LanguageEnglish
Published Elsevier B.V 2001
Subjects
Catalan paths
Combinatorics
Combinatorics
Catalan paths
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Summary:A Catalan path of length n, is a path from (0,0) going N=(0,1) or E=(0,1) in each step, such that it stays under (or on) the line x= y and ending at ( n, n) after 2 n steps. Here we calculate the total area between the line y= x and all Catalan paths. The total area a n= 1 2 ∑ k=1 nc k4 n−k , where c k is the number of Catalan paths of length k.
ISSN:0012-365X
1872-681X
DOI:10.1016/S0012-365X(00)00162-X