By a Narayana-enumerated object I mean an object whose count is given by the Narayana number $N(n,k)=\frac{1}{n} {n \choose k} {n \choose k-1}$. Can you give me a reference to some good big list of Narayana-enumerated objects? I have found two Narayana-enumerated objects (the two objects being closely related one to another) and would like to see whether my two objects are in the list.



A big list of Narayana-enumerated objects
[Elements of the sets enumerated by super-Catalan numbers](http://math.haifa.ac.il/toufik/enumerative/supercat.pdf) contains many Narayana-enumerated objects. (The super-Catalan number $s\_n$ is related to the Narayana numbers by $s\_n=\sum\_{k=1}^n 2^{k-1}N\_{n,k}$.)


Some examples:


The following five parameters of Dyck paths are enumerated by Narayana numbers:  

(i) number of high peaks;  

(ii)number of valleys;  

(iii)number of doublerises;  

(iv) number of rises at an even level;  

(v) number of nonfinal ascents and descents of length greater than 1.


132-avoiding permutations with given number excedances ($a\_i > i$) are counted by Narayana numbers, as well as those with given number descents ($a\_i<i$).


