Geodesic
Latin squares with forbidden entries
The electronic journal of combinatorics, Tome 13 (2006)
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An $n \times n$ array is avoidable if there exists a Latin square which differs from the array in every cell. The main aim of this paper is to present a generalization of a result of Chetwynd and Rhodes involving avoiding arrays with multiple entries in each cell. They proved a result regarding arrays with at most two entries in each cell, and we generalize their method to obtain a similar result for arrays with arbitrarily many entries per cell. In particular, we prove that if $m\in {\Bbb N}$, there exists an $N=N(m)$ such that if $F$ is an $N\times N$ array with at most $m$ entries in each cell, then $F$ is avoidable.
DOI : 10.37236/1073
Classification : 05B15, 05C70 
@article{10_37236_1073,
     author = {Jonathan Cutler and Lars-Daniel \"Ohman},
     title = {Latin squares with forbidden entries},
     journal = {The electronic journal of combinatorics},
     year = {2006},
     volume = {13},
     doi = {10.37236/1073},
     zbl = {1098.05016},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1073/}
}
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%A Lars-Daniel Öhman
%T Latin squares with forbidden entries
%J The electronic journal of combinatorics
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%F 10_37236_1073
Jonathan Cutler; Lars-Daniel Öhman. Latin squares with forbidden entries. The electronic journal of combinatorics, Tome 13 (2006). doi: 10.37236/1073

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