The excedance algebra

Motivated by the excedance set statistic, we define the excedance algebra as the quotient algebra k 〈 a , b 〉 / ( b a − a b − a − b ) . We examine the expansion of any monomial in terms of the linear basis a m b n using alternating tableaux and shift invariant operators. As a result we obtain a new combinatorial interpretation of the coefficients of the Gandhi polynomials.