Stanley's character polynomials and coloured factorizations in the symmetric group

Abstract

Stanley introduces polynomials which help evaluate symmetric group characters and conjectures that the coefficients of the polynomials are positive. Stanley later gives a conjectured combinatorial interpretation for the coefficients of the polynomials. Here, we prove the conjecture for the terms of highest degree.

11 pages, 5 figures, v2 minor revisions (typos etc)

References in corpus (1)

• A conjectured combinatorial interpretation of the normalized irreducible character values of the symmetric group