Given a permutation $\pi$ we can write $\pi=s_{i_1} ... s_{i_l}$ as a product of simple transpositions $s_i=(i,i+1)$ in a minimal way.

Question 1: Is there an "official" name for the permutation statistic given by the cardinality of the set $\{i_1,...,i_l \}$ ? (such as Coxeter length seems to be the official name for $l$)

See http://www.findstat.org/StatisticsDatabase/St000019 for this statistic.

Question 2: Is there a reference that the generating function for this permutation statistic restricted to 321-avoiding permutations is given by Catalan's triangle: http://oeis.org/A009766 ?