Hi guys just a quick questions
What are the real life application of catalan numbers?
Thanks a lot!



Application of Catalan number
In all seriousness, this type of enumerative combinatorics is very useful e.g. in figuring out expected running time for computer programs. An example involving Catalan numbers (which may seem a little contrived, but I think things like this probably do really come up) is: count how many times you go through the inner loop, i.e. how many times you print "hello world", in:


for $i\_1=0$ to $1$


for $i\_2=i\_1$ to $2$


for $i\_3=i\_2$ to $3$


...


for $i\_n = i\_{n-1}$ to $n$


print "hello world"


