Chromatic classical symmetric functions
نویسندگان
چکیده
In this note we classify when a skew Schur function is a positive linear combination of power sum symmetric functions. We then use this to determine precisely when any scalar multiple of a skew Schur function is the chromatic symmetric function of some graph. As a consequence we prove that of the classical bases for symmetric functions only certain scalar multiples of the elementary symmetric functions can be realised as the chromatic symmetric function of some graph, namely a particular union of complete graphs.
منابع مشابه
Chromatic Bases for Symmetric Functions
In this note we obtain numerous new bases for the algebra of symmetric functions whose generators are chromatic symmetric functions. More precisely, if {Gk}k>1 is a set of connected graphs such that Gk has k vertices for each k, then the set of all chromatic symmetric functions {XGk}k>1 generates the algebra of symmetric functions. We also obtain explicit expressions for the generators arising ...
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1. Definitions and a main result 2 1.1. Graphs and colorings . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2. Symmetric functions . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3. Chromatic symmetric functions . . . . . . . . . . . . . . . . . . . . . 5 1.4. Connected components . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.5. Circuits and broken circuits . . . . ...
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تاریخ انتشار 2016