q-Narayana numbers and the flag h-vector of J(2?n)

The Narayana numbers are N(n, k) = 1 n ( n k )( n k+1 ) . There are several natural statistics on Dyck paths with a distribution given by N(n, k). We show the equidistribution of Narayana statistics by computing the flag h-vector of J(2×n) in different ways. In the process we discover new Narayana statistics and provide co-statistics for which the Narayana statistics in question have a distribution given by Fürlinger and Hofbauers q-Narayana numbers. We also interpret the h-vector in terms of semi-standard Young tableaux, which enables us to express the q-Narayana numbers in terms of Schur functions.