The Catalan numbers are in bijection with the 123, 132, etc. avoiding permutations in $S_n$. If we move to type B, the type B Catalan numbers is $\binom{2n}{n}$, and the permutation group is the hyperoctahedral group of signed permutations $\pm[n]$. Is there a natural bijection between the type B Catalan numbers and a choice of elements of the hyperoctahedral group?
Note: Maybe this is clear if someone knows where the type B Catalan number comes from. I would also be appreciative of any (preferably freely available) resources that discuss Catalan numbers of different Coxeter types.