Littlewood–Richardson rules for symmetric skew quasisymmetric Schur functions

The classical Littlewood–Richardson rule is a rule for computing coefficients in many areas, and comes in many guises. In this paper we prove two Littlewood–Richardson rules for symmetric skew quasisymmetric Schur functions that are analogous to the famed version of the classical Littlewood–Richardson rule involving Yamanouchi words. Furthermore, both our rules contain this classical Littlewood–Richardson rule as a special case. We then apply our rules to combinatorially classify symmetric skew quasisymmetric Schur functions. This answers affirmatively a conjecture of Bessenrodt, Luoto and van Willigenburg.