Yang Hui Type Magic Squares with $t$-Powered Sum

Abstract

In this paper, the existence of Yang Hui type magic squares of order $n$ with $t$-powered sum (YMS($n$, $t$)) for general $t$ is investigated. Some constructions of YMS($n$, $t$) are obtained by using strongly symmetric self-orthogonal diagonal Latin squares and magic rectangles. Applying these constructions, it is proved that for an integer $t>1$ there exist both a symmetric elementary YMS($2^t$, $2t–2$) and a symmetric elementary YMS($2^t–k$, $2t$) for odd $k>1$, which improves the known result on YMSs.