Area of Catalan paths on a checkerboard

Szu En Cheng; Sen Peng Eu; Tung Shan Fu

doi:10.1016/j.ejc.2006.01.006

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 journal › Article › peer-review

11 Citations (Scopus)

Abstract

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 language	English
Pages (from-to)	1331-1344
Number of pages	14
Journal	European Journal of Combinatorics
Volume	28
Issue number	4
DOIs	https://doi.org/10.1016/j.ejc.2006.01.006
Publication status	Published - 2007 May
Externally published	Yes

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics

Access to Document

10.1016/j.ejc.2006.01.006

Cite this

@article{0df4f6f7e9534b61ae13788e92bd0ddb,

title = "Area of Catalan paths on a checkerboard",

abstract = "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.",

author = "Cheng, \{Szu En\} and Eu, \{Sen Peng\} and Fu, \{Tung Shan\}",

note = "Funding Information: The authors would like to thank Professor Louis Shapiro for useful suggestions during his visit to Academia Sinica, Taiwan, and thank the referees for helpful remarks. The authors are partially supported by the National Science Council, Taiwan, under grants NSC 93-2115-M-390-006 (S.-E. Cheng), NSC 94-2115-M-390-005 (S.-P. Eu), and NSC 94-2115-M-251-001 (T.-S. Fu).",

year = "2007",

month = may,

doi = "10.1016/j.ejc.2006.01.006",

language = "English",

volume = "28",

pages = "1331--1344",

journal = "European Journal of Combinatorics",

issn = "0195-6698",

publisher = "Academic Press",

number = "4",

}

TY - JOUR

T1 - Area of Catalan paths on a checkerboard

AU - Cheng, Szu En

AU - Eu, Sen Peng

AU - Fu, Tung Shan

N1 - Funding Information: The authors would like to thank Professor Louis Shapiro for useful suggestions during his visit to Academia Sinica, Taiwan, and thank the referees for helpful remarks. The authors are partially supported by the National Science Council, Taiwan, under grants NSC 93-2115-M-390-006 (S.-E. Cheng), NSC 94-2115-M-390-005 (S.-P. Eu), and NSC 94-2115-M-251-001 (T.-S. Fu).

PY - 2007/5

Y1 - 2007/5

N2 - 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.

AB - 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.

UR - https://www.scopus.com/pages/publications/33847621264

UR - https://www.scopus.com/pages/publications/33847621264#tab=citedBy

U2 - 10.1016/j.ejc.2006.01.006

DO - 10.1016/j.ejc.2006.01.006

M3 - Article

AN - SCOPUS:33847621264

SN - 0195-6698

VL - 28

SP - 1331

EP - 1344

JO - European Journal of Combinatorics

JF - European Journal of Combinatorics

IS - 4

ER -

Area of Catalan paths on a checkerboard

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this