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

^*此作品的通信作者

研究成果: 會議貢獻類型 › 會議論文 › 同行評審

摘要

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.

原文	英語
頁面	387-397
頁數	11
出版狀態	已發佈 - 2006
對外發佈	是
事件	18th Annual International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2006 - San Diego, CA, 美国持續時間: 2006 6月 19 → 2006 6月 23

其他

其他	18th Annual International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2006
國家/地區	美国
城市	San Diego, CA
期間	2006/06/19 → 2006/06/23

ASJC Scopus subject areas

代數與數理論

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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",

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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

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AN - SCOPUS:84860617664

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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

摘要

其他

ASJC Scopus subject areas

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