AN APPLICATION OF THE COMBINATORIAL RIEMANN-ROCH THEOREM TO THE EHRHART POLYNOMIAL OF INTEGRAL POLYTOPES IN RD

被引：0

作者：

KANTOR, JM ^{[1
]}

KHOVANSKII, A ^{[1
]}

机构：

[1] ACAD SCI,INST ETUD SYST,MOSCOW 117312,RUSSIA

来源：

COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE | 1993年 / 317卷 / 05期

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D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The combinatorial Riemann-Roch theorem ([8], [9], [6]) relates the volume of an integral polytope to the number of integral points in it. This is only valid for polytopes with primitive fan (the associated toric variety is regular). However, applying this result in a suitable manner, we deduce an explicit formula for the coefficient of degree (d- 2) of the Ehrhart polynomial of any integral polytope in R(d). In particular this gives a general formula for the number of integral points in any integral polytope in R4, a new geometric look at the introduction of Dedekind sums in these questions.

引用

页码：501 / 507

页数：7

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