The aß-construction of magic hypercubes

被引：0
|
作者：
Arroyo, Joshua [1 ]
Holder, Leanne [2 ]
机构：
[1] Univ Florida, Dept Math, Gainseville, FL 32611 USA
[2] Rose Hulman Inst Technol, Dept Math, Terre Haute, IN 47803 USA
来源：
INVOLVE, A JOURNAL OF MATHEMATICS | 2022年 / 15卷 / 03期
关键词：
magic cube; magic hypercube;
D O I：
10.2140/involve.2022.15.393
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A magic hypercube of dimension m and order n is an nm array filled with nm distinct positive integers 1, 2,..., n(m) such that the entries in each of the mn(m-1) hyperrows and the 2(m-1) space diagonals sum to the same number, the magic sum. We present the alpha ss-construction which follows an algorithm which places entries into a hypercube by moving along permutations of the vector <alpha, 0,..., 0, ss >. Under certain restrictions, this construction creates odd-ordered magic hypercubes.
引用
收藏
页码：393 / 410
页数：18
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