Geodesic
Induced subarrays of Latin squares without repeated symbols
R. Julian R. Abel1 ; Nicholas J. Cavenagh2 ; Jaromy Kuhl3
1University of New South Wales
2University of Waikato
3University of West Florida
The electronic journal of combinatorics, Tome 20 (2013) no. 1
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We show that for any Latin square $L$ of order $2m$, we can partition the rows and columns of $L$ into pairs so that at most $(m+3)/2$ of the $2\times 2$ subarrays induced contain a repeated symbol. We conjecture that any Latin square of order $2m$ (where $m\geq 2$, with exactly five transposition class exceptions of order $6$) has such a partition so that every $2\times 2$ subarray induced contains no repeated symbol. We verify this conjecture by computer when $m\leq 4$.
DOI : 10.37236/2372
Classification : 05B15
Mots-clés : Latin square, 2-partition, conjugate, isotopic, transposition class, \(k\)-partition, discrepancy, potential

R. Julian R. Abel  1   ; Nicholas J. Cavenagh  2   ; Jaromy Kuhl  3

1 University of New South Wales
2 University of Waikato
3 University of West Florida 
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     title = {Induced subarrays of {Latin} squares without repeated symbols},
     journal = {The electronic journal of combinatorics},
     year = {2013},
     volume = {20},
     number = {1},
     doi = {10.37236/2372},
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R. Julian R. Abel; Nicholas J. Cavenagh; Jaromy Kuhl. Induced subarrays of Latin squares without repeated symbols. The electronic journal of combinatorics, Tome 20 (2013) no. 1. doi: 10.37236/2372

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