An enumeration problem related to Catalan number
Youlin Li · Journal of Lanzhou University · 2003
This paper deals with a kind of permutation which can be formed from n 1 A 1,n 2 A 2 and n 3 A 3(n 1≥n 2≥n 3≥0), satisfying that from the left end to each term the number of A 1 is no less than the number of A i+1(i=1,2).Using inclusion and exclusion principle, we find the number of this kind of permutation, which is n 1+n 2+n 3 n 1,n 2,n 31-n 2n 1+1-n 3n 2+1+n 3(n 2(n 2-n 3+2)+(n 3-1)(n 1+1))(n 2+1)(n 1+1)(n 1+2). And especially when n 1=n 2=n 3=n the number is 2(n+1)2(n+2)3n n,n,n.