Truncated homogeneous symmetric functions

Abstract

Extending the elementary and complete homogeneous symmetric functions, we introduce the truncated homogeneous symmetric function in (1) for any integer partition λ, and show that the transition matrix from to the power sum symmetric functions is given by where and z are nonsingular diagonal matrices. Consequently, forms a basis of the ring Λ of symmetric functions. In addition, we show that the generating function satisfies where ω is the involution of Λ sending each elementary symmetric function to the complete homogeneous symmetric function .