Stanley’s character polynomials and coloured factorizations in the symmetric group
نویسنده
چکیده
In Stanley [8], the author introduces polynomials which help evaluate symmetric group characters and conjectures that the coefficients of the polynomials are positive. In [9], the same author gives a conjectured combinatorial interpretation for the coefficients of the polynomials. Here, we prove the conjecture for the terms of highest degree.
منابع مشابه
Positivity results for Stanley’s character polynomials
In Stanley [16], the author introduces expressions for the normalized characters of the symmetric group and states 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 in Goulden and Rattan [7]. We shall see that the...
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A theorem due to Tokuyama expresses Schur polynomials in terms of GelfandTsetlin patterns, providing a deformation of the Weyl character formula and two other classical results, Stanley’s formula for the Schur q-polynomials and Gelfand’s parametrization for the Schur polynomials. We generalize Tokuyama’s formula to the Hall-Littlewood polynomials by extending Tokuyama’s statistics. Our result, ...
متن کاملStanley's character polynomials and coloured factorisations in the symmetric group
In Stanley [8] the author introduces polynomials which help evaluate symmetric group characters and conjectures that the coefficients of the polynomials are positive. In [9] the same author gives a conjectured combinatorial interpretation for the coefficients of the polynomials. Here, we prove the conjecture for the terms of highest degree.
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In recent years we have worked on a project involving poset topology, various analogues of Eulerian polynomials, and a refinement of Richard Stanley’s chromatic symmetric function. Here we discuss how Stanley’s ideas and results have influenced and inspired our own work. 1. A walk in the woods It is a privilege and an honor to contribute an article to a volume celebrating Richard Stanley’s 70th...
متن کاملA positivity conjecture for Jack polynomials
We present a positivity conjecture for the coefficients of the development of Jack polynomials in terms of power sums. This extends Stanley’s ex-conjecture about normalized characters of the symmetric group. We prove this conjecture for partitions having a rectangular shape.
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تاریخ انتشار 2007