Positivity Theorems for Solid-Angle Polynomials

نویسنده

  • Matthias Beck
چکیده

For a lattice polytope P , define AP(t) as the sum of the solid angles of all the integer points in the dilate tP . Ehrhart and Macdonald proved that AP(t) is a polynomial in the positive integer variable t. We study the numerator polynomial of the solid-angle series ∑ t≥0 AP(t)z . In particular, we examine nonnegativity of its coefficients, monotonicity and unimodality questions, and study extremal behavior of the sum of solid angles at vertices of simplices. Some of our results extend to more general valuations.

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تاریخ انتشار 2009