Skew key polynomials and a generalized Littlewood–Richardson rule

Young’s lattice is a partial order on integer partitions whose saturated chains correspond to standard Young tableaux, one type of combinatorial object that generates the Schur basis for symmetric functions. Generalizing lattice, we introduce new weak compositions call key poset. Saturated in this poset objects generate polynomials, nonsymmetric polynomial generalization basis. skew functions, define polynomials terms Using dual equivalence, give nonnegative composition Littlewood–Richardson rule expansion generalizing flagged Reiner and Shimozono.