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 -