The Euler-Catalan identity (Q1110512)

The author derives a recurrence relation for \(\sum_{\sigma \in S_ n}t^{d(\sigma)}q^{m(\sigma)}p^{i(\sigma)}u^{a(\sigma)}v^{b(\sigma)}\) which is a common generalization of recurrence relations of Euler numbers and Catalan numbers. Here d(\(\sigma)\) is the descent number, m(\(\sigma)\) is the major index, i(\(\sigma)\) is the inversion number, a(\(\sigma)\) and b(\(\sigma)\) count some 3-letter patterns. The recurrence relation also provides formulae for q-Catalan and q-Euler numbers.