Enumeration On Amajor Index Of Row-increasing Tableaux Of Shape 2×n

Young tableaux are important research object in enumerative combinatorics.Recently O.Pechenik studied the cyclic sieving of increasing tableaux of shape 2 × n,and obtained a polynomial on the major index of these tableaux,which is a q-analogue of refined small Schr ?der numbers.Ruoxia Du and Xiaojie Fan studied the counting problem about the major index of row-increasing tableaux of shape2 × n,which is a q-analogue of refined large Schr ?der numbers.We define prime row-increasing tableaux and study the amajor index of prime row-increasing tableaux of shape 2 × n.We construct a bijection which shows a relationship between the major index polynomial and the amajor index polynomial of row-increasing tableaux.Combining our work with existing result,we get the amajor index polynomial for row-increasing tableaux.