magic (version 1.5-9)

sam: Sparse antimagic squares

Description

Produces an antimagic square of order \(m\) using Gray and MacDougall's method.

Usage

sam(m, u, A=NULL, B=A)

Arguments

m

Order of the magic square (not “n”: the terminology follows Gray and MacDougall)

u

See details section

A,B

Start latin squares, with default NULL meaning to use circulant(m)

Details

In Gray's terminology, sam(m,n) produces a \(SAM(2m,2u+1,0)\).

The method is not vectorized.

To test for these properties, use functions such as is.antimagic(), documented under is.magic.Rd.

References

I. D. Gray and J. A. MacDougall 2006. “Sparse anti-magic squares and vertex-magic labelings of bipartite graphs”, Discrete Mathematics, volume 306, pp2878-2892

See Also

magic,is.magic

Examples

Run this code
# NOT RUN {
sam(6,2)

jj <- matrix(c(
     5, 2, 3, 4, 1,
     3, 5, 4, 1, 2,
     2, 3, 1, 5, 4,
     4, 1, 2, 3, 5, 
     1, 4, 5, 2, 3),5,5)

is.sam(sam(5,2,B=jj))

# }

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