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Complete diagonals of Latin squares

1979
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Canadian mathematical bulletin
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J. Marica and J. Schônhein [4], using a theorem of M. Hall, Jr. [3], see below, proved that if any n-1 arbitrarily chosen elements of the diagonal of an nxn array are prescribed, it is possible to complete the array to form an n x n latin square. This result answers affirmatively a special case of a conjecture of T. Evans [2] , to the effect that an n x n incomplete latin square with at most n-1 places occupied can be completed to an nxn latin square. When the complete diagonal is prescribed,

doi:10.4153/cmb-1979-062-3
fatcat:m4sad7lhdnbwnkzgwd2kpvx4ee