Noncommutative symmetric functions and skewing operators

Skewing operators play a central role in the symmetric function theory because of the importance of the product structure of the symmetric function space. The theory of noncommutative symmetric functions is a useful tool for studying expansions of a given symmetric function in terms of various bases. In this paper, we establish a further development of the theory for studying skewing operators. Using this machinery, we are able to easily reproduce the Littlewood–Richardson rule and provide recurrence relations for chromatic quasisymmetric functions, which generalize Harada–Precup's recurrence.