PISOT NUMBERS AND CHROMATIC ZEROS
PISOT NUMBERS AND CHROMATIC ZEROS
In this article we show that Pisot numbers of even degree and their powers cannot be roots of chromatic polynomials. We also consider the family of smallest Pisot numbers of odd degree. We show that they cannot be roots of chromatic polynomials of connected graphs with a certain maximum number of vertices.
Partitions; congruences and congruential restrictions, PV-numbers and generalizations; other special algebraic numbers; Mahler measure, Pisot number, chromatic zero, connected graph, Exact enumeration problems, generating functions, Algebraic numbers; rings of algebraic integers, even degree
Partitions; congruences and congruential restrictions, PV-numbers and generalizations; other special algebraic numbers; Mahler measure, Pisot number, chromatic zero, connected graph, Exact enumeration problems, generating functions, Algebraic numbers; rings of algebraic integers, even degree
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