The dimension of magic squares over fields of characteristics two and three

초록

Hou et al. [4] have studied various spaces of magic squares over a field F and determined their dimensions. However, they left one open question unsolved, namely, if the characteristic of F is 2 or 3, exactly which n and k make M-n,M-k (1) nonempty, where M-n,M-k (1) denotes the set of all n x n matrices over F whose row sums, column sums, k diagonal sums, and k antidiagonal sums are all 1. We solve this completely. (C) 2015 Elsevier Inc. All rights reserved.

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