منابع مشابه
Enumeration of 4 x 4 magic squares
A magic square is an n × n array of distinct positive integers whose sum along any row, column, or main diagonal is the same number. We compute the number of such squares for n = 4, as a function of either the magic sum or an upper bound on the entries. The previous record for both functions was the n = 3 case. Our methods are based on inside-out polytopes, i.e., the combination of hyperplane a...
متن کاملEnumeration of 4× 4 Magic Squares
A magic square is an n × n array of distinct positive integers whose sum along any row, column, or main diagonal is the same number. We compute the number of such squares for n = 4, as a function of either the magic sum or an upper bound on the entries. The previous record for both functions was the n = 3 case. Our methods are based on inside-out polytopes, i.e., the combination of hyperplane a...
متن کاملConstructing all magic squares of order three
A magic square of order n is an n by n matrix with distinct nonnegative integer entries such that every row sum, column sum, and (two) diagonal sums equals to the same number m, the magic number. Adding 1 to every entry will give us a traditional magic square of positive integers. A magic square is pure if the entries are the consecutive numbers from 0 to n − 1, and hence it has magic number 3 ...
متن کاملEven Order Regular Magic Squares Are Singular
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متن کاملINTEGER-MAGIC SPECTRA OF CYCLE RELATED GRAPHS
For any h in N , a graph G = (V, E) is said to be h-magic if there exists a labeling l: E(G) to Z_{h}-{0} such that the induced vertex set labeling l^{+: V(G) to Z_{h}} defined by l^{+}(v)= Summation of l(uv)such that e=uvin in E(G) is a constant map. For a given graph G, the set of all for which G is h-magic is called the integer-magic spectrum of G and is denoted by IM(G). In this paper, the ...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2014
ISSN: 0024-3795
DOI: 10.1016/j.laa.2014.05.038