Positivity results for Stanley's character polynomials
Abstract
Description
Stanley introduced expressions for the normalized characters of the symmetric group and stated some positivity conjectures for these expressions. Here, we give an affirmative partial answer to Stanley's positivity conjectures about the expressions using results on Kerov polynomials. In particular, we use new positivity results by Goulden and the present author. We shall see that the generating series $C(t)$ introduced by them is critical to our discussion.
20 pages, 2 figures, v2, minor revisions, fixed typos etc
20 pages, 2 figures, v2, minor revisions, fixed typos etc