Area of Catalan paths on a checkerboard

Szu En Cheng*, Sen Peng Eu, Tung Shan Fu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)


It is known that the area of all Catalan paths of length n is equal to 4n - fenced(frac(2 n + 1, n)), which coincides with the number of inversions of all 321-avoiding permutations of length n + 1. In this paper, a bijection between the two sets is established. Meanwhile, a number of interesting bijective results that pave the way to the required bijection are presented.

Original languageEnglish
Pages (from-to)1331-1344
Number of pages14
JournalEuropean Journal of Combinatorics
Issue number4
Publication statusPublished - 2007 May
Externally publishedYes

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics


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