Premature partial latin squares.
Premature partial latin squares.
A partial Latin square of order \(n\), \(\text{PLS}(n)\), is an \(n\times n\) array whose cells are either empty, or contain an entry of \(N=\{1,2,\dots ,n\}\) such that each element occurs in at most one cell in each row and each column. A \(\text{PLS}(n)\) is completable if the empty cells can be filled with symbols of \(N\) such that a Latin square of order \(n\) results. A \(\text{PLS}(n)\) is premature if it is not completable but removing any of its entries results in a completable \(\text{PLS}(n)\). The spectrum of a premature \(\text{PLS}(n)\) is a set \(P(n)=\{t\mid \text{there exists a premature }\text{PLS}(n)\text{ with exactly }t\text{ nonempty cells}\}\). The results of the paper give several properties of spectra of premature PLSs and constructions of premature PLSs.
- University of Newcastle Australia Australia
integers, partial latin square, Orthogonal arrays, Latin squares, Room squares, latin square, partial latin squares (PLS), premature, spectrum
integers, partial latin square, Orthogonal arrays, Latin squares, Room squares, latin square, partial latin squares (PLS), premature, spectrum
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