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- W1567697449 abstract "For a lattice polytope P, define A_P(t) as the sum of the solid angles of all the integer points in the dilate tP. Ehrhart and Macdonald proved that A_P(t) is a polynomial in the positive integer variable t. We study the numerator polynomial of the solid-angle series sum_{t >= 0} A_P(t) z^t. 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." @default.
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- W1567697449 date "2009-06-22" @default.
- W1567697449 modified "2023-09-27" @default.
- W1567697449 title "Positivity theorems for solid-angle polynomials" @default.
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