Discrete Math Seminar: A notion of transpose for compositions

The omega transformation takes a Schur function indexed by a partition to the Schur function indexed by the partition's transpose. In this joint work with Jeff Remmel, we explore a refinement of the omega transformation defined on the quasisymmetric Schur functions. The resulting polynomials are called row-strict quasisymmetric Schur functions since they are described combinatorially as generating functions for row-strict composition tableaux. The interaction between row-strict quasisymmetric Schur functions and quasisymmetric Schur functions provides a natural method for interpolating between the compositions that rearrange a given partition and those that rearrange the partition's transpose. This allows us to define an operation on compositions which is similar to the transposition operation on partitions.