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SOMA


Let k>=0 and n>=2 be integers. A SOMA, or more specifically a SOMA(k,n), is an n×n array A, whose entries are k-subsets of a kn-set Omega, such that each element of Omega occurs exactly once in each row and exactly once in each column of A, and no 2-subset of Omega is contained in more than one entry of A (Soicher 1999).

A SOMA(k,n) can be constructed by superposing k mutually orthogonal Latin squares of order n with pairwise disjoint symbol-sets, and so a SOMA(k,n) can be seen as a generalization of k mutually orthogonal Latin squares of order n.


See also

Latin Square, Soma Cube

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References

Soicher, L. H. "On the Structure and Classification of SOMAs: Generalizations of Mutually Orthogonal Latin Squares." Electronic J. Combinatorics 6, No. 1, R32, 1-15, 1999. http://www.combinatorics.org/Volume_6/Abstracts/v6i1r32.html.

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SOMA

Cite this as:

Weisstein, Eric W. "SOMA." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SOMA.html

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