Area of Catalan paths on a checkerboard

Szu En Cheng, Sen Peng Eu, Tung Shan Fu

Research output: Contribution to conferencePaper

Abstract

It is known that the area of all Catalan paths of length n is equal to 4n - ( 2n+1), 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
Pages387-397
Number of pages11
Publication statusPublished - 2006 Dec 1
Event18th Annual International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2006 - San Diego, CA, United States
Duration: 2006 Jun 192006 Jun 23

Other

Other18th Annual International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2006
CountryUnited States
CitySan Diego, CA
Period06/6/1906/6/23

Keywords

  • Catalan paths
  • Inversions
  • Permutations
  • Polyominoes

ASJC Scopus subject areas

  • Algebra and Number Theory

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  • Cite this

    Cheng, S. E., Eu, S. P., & Fu, T. S. (2006). Area of Catalan paths on a checkerboard. 387-397. Paper presented at 18th Annual International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2006, San Diego, CA, United States.