Brick tabloids and the connection matrices between bases of symmetric functions

Egecioglu, ii. and J.B. Remmel, Brick tabloids and the connection matrices between bases of symmetric functions, Discrete Applied Mathematics 34 (1991) 107-120. Let H, denote the space of symmetric functions, homogeneous of degree n. In this paper we introduce a new set of combinatorial objects called I-brick tabloids and its variants, which we use *to give combinatorial interpretations of the entries for twelve of the transition matrices between natural bases of H,. Using these interpretations, it is possible to give purely combinatorial proofs of various identities between these connection matrices. Also as a consequence, the so called forgotten basis of Doubilet and Rota is shown to admit a natural combinatorial description in terms of brick tabloids and the monomial symmetric functions.