f-VECTORS OF BARYCENTRIC SUBDIVISIONS

نویسندگان

  • FRANCESCO BRENTI
  • VOLKMAR WELKER
چکیده

For a simplicial complex or more generally Boolean cell complex ∆ we study the behavior of the f and h-vector under barycentric subdivision. We show that if ∆ has a non-negative h-vector then the h-polynomial of its barycentric subdivision has only simple and real zeros. As a consequence this implies a strong version of the Charney-Davis conjecture for spheres that are the subdivision of a Boolean cell complex or the subdivision of the boundary complex of a simple polytope. For a general (d − 1)-dimensional simplicial complex ∆ the hpolynomial of its n-th iterated subdivision shows convergent behavior. More precisely, we show that among the zeros of this hpolynomial there is one converging to infinity and the other d− 1 converge to a set of d− 1 real numbers which only depends on d.

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تاریخ انتشار 2007