Enumeration On Row-increasing Tableaux Of Shape 2×n

Young tableaux are important combinatorial objects in enumerative combinatorics,and they are widely used in other mathematical branches such as representation theory and al-gebraic geometry.O.Pechenik study the cyclic sieving phenomenon of increasing tableaux and obtain a q-analog of small Schroder number.In this article,we enumerate increas-ing tableaux and row increasing tableaux and study the major index of these two kinds of tableaux.In the first part,we count increasing tableaux and row increasing tableaux of shape(2 x n).In the second part,we study the major index of increasing tableaux,obtain the q-analog of small Schroder number again.Then we give bijection between increasing tableaux and row increasing tableaux,discuss the major index of row increasing tableaux and obtain a q-analog of large Schroder number.