R: Sparse antimagic squares

sam {magic} | R Documentation

## 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`.

### Author(s)

Robin K. S. Hankin

### 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

    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))

[Package magic version 1.5-8 Index]