In 1975 Stein conjectured that in every n×n array filled with the numbers 1,…,n with every number occuring exactly n times, there is a partial transversal of size n − 1. In this note we show that this conjecture is false by constructing such arrays without partial transverals of size n − (ln n)/42
A well known result of Fraenkel and Simpson states that the number of distinct squares in a word of ...
AbstractIt is well known that if n is even, the addition table for the integers modulo n (which we d...
AbstractThe enumeration problem of Latin rectangles is formulated in terms of permanents, and two ‘h...
In 1975 Stein conjectured that in every n × n array filled with the numbers 1, . . . , n with every...
In 1975 Stein conjectured that in every n × n array filled with the numbers 1,...,n with every numbe...
In 1975 Stein conjectured that in every n×n array filled with the numbers 1,…,n with every number oc...
AbstractIt is proved that every n×n Latin square has a partial transversal of length at least n−O(lo...
AbstractIt is proved that every n × n Latin square has a partial transversal of length at least n − ...
AbstractIn this paper it is shown that every m×n array in which each symbol appears at most (mn-1)/(...
The full n-Latin square is the n×n array with symbols 1, 2, . . . , n in each cell. In this paper we...
AbstractWe investigate transversals of rectangular arrays. For positive integers m and n, where 2⩽m⩽...
A Latin square is reduced if its first row and column are in natural order. For Latin squares of a p...
A “Latin square of order n” is an “n by n” array of the symbols 1, 2, ... , n, such that each symbol...
A well known result of Fraenkel and Simpson states that the number of distinct squares in a word of ...
AbstractThe notion of partial transversal in a Latin square is defined. A proof is given of the exis...
A well known result of Fraenkel and Simpson states that the number of distinct squares in a word of ...
AbstractIt is well known that if n is even, the addition table for the integers modulo n (which we d...
AbstractThe enumeration problem of Latin rectangles is formulated in terms of permanents, and two ‘h...
In 1975 Stein conjectured that in every n × n array filled with the numbers 1, . . . , n with every...
In 1975 Stein conjectured that in every n × n array filled with the numbers 1,...,n with every numbe...
In 1975 Stein conjectured that in every n×n array filled with the numbers 1,…,n with every number oc...
AbstractIt is proved that every n×n Latin square has a partial transversal of length at least n−O(lo...
AbstractIt is proved that every n × n Latin square has a partial transversal of length at least n − ...
AbstractIn this paper it is shown that every m×n array in which each symbol appears at most (mn-1)/(...
The full n-Latin square is the n×n array with symbols 1, 2, . . . , n in each cell. In this paper we...
AbstractWe investigate transversals of rectangular arrays. For positive integers m and n, where 2⩽m⩽...
A Latin square is reduced if its first row and column are in natural order. For Latin squares of a p...
A “Latin square of order n” is an “n by n” array of the symbols 1, 2, ... , n, such that each symbol...
A well known result of Fraenkel and Simpson states that the number of distinct squares in a word of ...
AbstractThe notion of partial transversal in a Latin square is defined. A proof is given of the exis...
A well known result of Fraenkel and Simpson states that the number of distinct squares in a word of ...
AbstractIt is well known that if n is even, the addition table for the integers modulo n (which we d...
AbstractThe enumeration problem of Latin rectangles is formulated in terms of permanents, and two ‘h...
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