Roots of Ehrhart polynomials of Gorenstein Fano polytopes

Given arbitrary integers $k$ and $d$ with $0 \leq 2 k \leq d$ , we construct a Gorenstein Fano polytope $\Pc \subset \RR^{d}$ of dimension $d$ such that (i) its Ehrhart polynomial $i (\Pc, n)$ possesses $d$ distinct roots; (ii) $i (\Pc, n)$ possesses exactly $2 k$ imaginary roots; (iii) $i (\Pc, n)$ possesses exactly $d

2k $r e a l r o o t s; (i v) t h e r e a l p a r t o f e a c h o f t h e i m a g i n a r y r o o t s i s e q u a l t o$ - 1 / 2 $; (v) a l l o f t h e r e a l r o o t s b e l o n g t o t h e o p e n i n t e r v a l$ (-1, 0)$.

2k $r e a l r o o t s; (i v) t h e r e a l p a r t o f e a c h o f t h e i m a g i n a r y r o o t s i s e q u a l t o$ - 1 / 2 $; (v) a l l o f t h e r e a l r o o t s b e l o n g t o t h e o p e n i n t e r v a l$ (-1, 0)$.

Roots of Ehrhart polynomials of Gorenstein Fano polytopes

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Roots of Ehrhart polynomials of Gorenstein Fano polytopes

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Roots of Ehrhart polynomials of Gorenstein Fano polytopes

文献摘要

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|讲解博客

|AI智能校验

Roots of Ehrhart polynomials of Gorenstein Fano polytopes

文献摘要

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|讲解博客

|AI智能校验

讲解博客

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