THE NUMBER OF GRIDPOINTS ON HYPERPLANE SECTIONS OF THE d-DIMENSIONAL CUBE

被引：0

作者：

Abel, Ulrich ^{[1
]}

机构：

[1] Tech Hsch Mittelhessen, Dept MND, Wilhelm Leuschner Str 13, D-61169 Friedberg, Germany

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2018年 / 146卷 / 12期

关键词：

SINC;

D O I：

10.1090/proc/14233

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We deduce a formula for the exact number of gridpoints (i.e., elements of Z(d)) in the extended d-dimensional cube nC(d) = [-n, +n](d) on intersecting hyperplanes. In the special case of the hyperplanes {x is an element of R-d vertical bar x(1) + ... + x(d) = b}, b is an element of Z, these numbers can be written as a finite sum involving products of certain binomial coefficients. Furthermore, we consider the limit as n tends to infinity which can be expressed in terms of Euler-Frobenius numbers. Finally, we state a conjecture on the asymptotic behaviour of this limit as the dimension d tends to infinity.

引用

页码：5349 / 5355

页数：7

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