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The $\alpha\beta$-construction of magic hypercubes

Joshua Arroyo and Leanne Holder

Vol. 15 (2022), No. 3, 393–410

A magic hypercube of dimension m and order n is an nm array filled with nm distinct positive integers 1,2,,nm such that the entries in each of the mnm1 hyperrows and the 2m1 space diagonals sum to the same number, the magic sum. We present the αβ-construction which follows an algorithm which places entries into a hypercube by moving along permutations of the vector α,0,,0,β. Under certain restrictions, this construction creates odd-ordered magic hypercubes.

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magic cube, magic hypercube
Mathematical Subject Classification
Primary: 05B30
Received: 10 September 2020
Revised: 11 November 2021
Accepted: 25 November 2021
Published: 2 December 2022

Communicated by Vadim Ponomarenko
Joshua Arroyo
Department of Mathematics
University of Florida
Gainseville, FL
United States
Leanne Holder
Department of Mathematics
Rose–Hulman Institute of Technology
Terre Haute, IN
United States