Chromatic symmetric function of graphs from Borcherds algebras release_6sqp4kxbl5cmxms3ncnm6e5u5q

by G. Arunkumar

Released as a article .

2019  

Abstract

Let g be a Borcherds algebra with the associated graph G. We prove that the chromatic symmetric function of G can be recovered from the Weyl denominator identity of g and this gives a Lie theoretic proof of Stanley's expression for chromatic symmetric function in terms of power sum symmetric function. Also, this gives an expression for chromatic symmetric function of G in terms of root multiplicities of g. The absolute value of the linear coefficient of the chromatic polynomial of G is known as the chromatic discriminant of G. As an application of our main theorem, we prove that graphs with different chromatic discriminants are distinguished by their chromatic symmetric functions. Also, we find a connection between the Weyl denominators and the G-elementary symmetric functions. Using this connection, we give a Lie theoretic proof of non-negativity of coefficients of G-power sum symmetric functions.
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Date   2019-08-22
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arXiv  1908.08198v1
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