Area of Catalan paths on a checkerboard

Szu En Cheng; Sen Peng Eu; Tung Shan Fu

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 conference › Paper › peer-review

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 language	English
Pages	387-397
Number of pages	11
Publication status	Published - 2006
Externally published	Yes
Event	18th Annual International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2006 - San Diego, CA, United States Duration: 2006 Jun 19 → 2006 Jun 23

Other

Other	18th Annual International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2006
Country/Territory	United States
City	San Diego, CA
Period	2006/06/19 → 2006/06/23

Keywords

Catalan paths
Inversions
Permutations
Polyominoes

ASJC Scopus subject areas

Algebra and Number Theory

Cite this

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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 - ( 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.",

keywords = "Catalan paths, Inversions, Permutations, Polyominoes",

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). ; 18th Annual International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2006 ; Conference date: 19-06-2006 Through 23-06-2006",

year = "2006",

language = "English",

pages = "387--397",

}

TY - CONF

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 - 2006

Y1 - 2006

N2 - 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.

AB - 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.

KW - Catalan paths

KW - Inversions

KW - Permutations

KW - Polyominoes

UR - https://www.scopus.com/pages/publications/84860617664

UR - https://www.scopus.com/pages/publications/84860617664#tab=citedBy

M3 - Paper

AN - SCOPUS:84860617664

SP - 387

EP - 397

T2 - 18th Annual International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2006

Y2 - 19 June 2006 through 23 June 2006

ER -

Area of Catalan paths on a checkerboard

Abstract

Other

Keywords

ASJC Scopus subject areas

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