2021/11/19 by Chanceley Book, Book, Chanceley, Abdollah Khodkar +1
Biochemistry, Genetics and Molecular Biology · Computer Science · Engineering · #05 #Combinatorics (math.CO) #DNA and Biological Computing #FOS: Mathematics #Graph Labeling and Dimension Problems #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2111.10334
openalex publication_date 2021/11/19 · openalex created_date 2022/05/05 · openalex updated_date 2026/08/04
A signed magic array, SMA(m, n;s,t), is an m × n array with the same number of filled cells s in each row and the same number of filled cells t in each column, filled with a certain set of numbers that is symmetric about the number zero, such that every row and column has a zero sum. We use the notation SMA(m, n) if m=t and n=s. In this paper, we prove that for every even number n≥ 2 there exists an SMA(m,n) such that the entries ± x appear in the same row for every x∈\1, 2, 3,…, mn/2\ if and only if m≡ 0, 3(\mod4) and n=2 or m≥ 3 and n≥ 4.