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On the zeros of independence and open set polynomials

Tuesday 22nd January 2008 - 11:30 to 12:00
INI Seminar Room 1

While the zeros of chromatic and flow polynomials have attracted much attention in the research literature, there are some other lesser known polynomials on discrete structures whose zeros are also worthy of investigation. Independence polynomials arise as generating functions of the number of independent sets of each cardinality in a graph. Open set polynomials enumerate open sets in a finite topology. We survey what is known about the nature and location of the zeros, with results ranging from bounds on the moduli to density and realness of the zeros, and even including a fractal or two thrown in for good measure.

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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons