Positivity results for Stanley's character polynomials

Details Positivity results for Stanley's character polynomials Positivity results for Stanley's character polynomials

2006-01-09

arxiv.org/abs/math/0601186v2

J. Algebra, 308(1):26-47, Feb. 2007

Mathematics

Representation Theory

20 pages, 2 figures, v2, minor revisions, fixed typos etc

Scientific paper

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.

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