Enumeration On Row-increasing Tableaux Of Two Rows

Young tableaux are important research objects in enumerative combinatorics.In this paper we study the enumeration on the major index polynomials for row-increasing tableaux of shape(n-a,a)with k repeating numbers.Firstly,we enumerate the major index polynomial for increasing tableaux of two rows and obtain the enumeration formulas.Secondly,we find a bijection between row-increasing tableaux of two rows and increasing tableaux of two rows,and further enumerate the major index polynomial for row-increasing tableaux of two rows and obtain the enumeration formulas.Finally,we find a bijection between rowincreasing tableaux of two rows and lattice path,then prove the enumeration formulas of row-increasing tableaux of two rows again by means of lattice path enumeration.