The main diagonal and the upper left-hand r × r square of an n × n array contain symbols, the remaining cells are empty. We give simple necessary and sufficient conditions for completing the array to a commutative Latin square. We apply these results to give a short proof of Cruse's theorem, and an embedding theorem for half-idempotent commutative Latin squares
International audienceThe completability of incomplete latin squares can be studied along two lines:...
The set PLS(a, b; n) is the set of all partial latin squares of order n with a completed rows, b com...
The set PLS(a, b; n) is the set of all partial latin squares of order n with a completed rows, b com...
The main diagonal and the upper left-hand r × r square of an n × n array contain symbols, the remain...
AbstractLet A be a Latin square of order n. Then the jth right diagonal of A is the set of n cells o...
We prove that an incomplete Latin square A of side r can be embedded in a Latin square of side n in ...
AbstractNecessary and sufficient conditions are obtained for the extendibility of an r × r symmetric...
AbstractWe present necessary and sufficient conditions for the embedding of a given incomplete latin...
We study the completion problem for simple k-Latin rectangles, which are a special case of the gener...
A diagonal Latin square of order n can be embedded in a diagonal Latin square of order t if and only...
AbstractAn incomplete double diagonal Latin square of order n can be double-diagonally embedded in a...
AbstractWe call a latin square A=(aij) of order n, aij∈{1,2,…,n}, right-diagonal-complete if {(aij,a...
Abstract. A classical question in combinatorics is the following: given a par-tial latin square P, w...
International audienceThe completability of incomplete latin squares can be studied along two lines:...
International audienceThe completability of incomplete latin squares can be studied along two lines:...
International audienceThe completability of incomplete latin squares can be studied along two lines:...
The set PLS(a, b; n) is the set of all partial latin squares of order n with a completed rows, b com...
The set PLS(a, b; n) is the set of all partial latin squares of order n with a completed rows, b com...
The main diagonal and the upper left-hand r × r square of an n × n array contain symbols, the remain...
AbstractLet A be a Latin square of order n. Then the jth right diagonal of A is the set of n cells o...
We prove that an incomplete Latin square A of side r can be embedded in a Latin square of side n in ...
AbstractNecessary and sufficient conditions are obtained for the extendibility of an r × r symmetric...
AbstractWe present necessary and sufficient conditions for the embedding of a given incomplete latin...
We study the completion problem for simple k-Latin rectangles, which are a special case of the gener...
A diagonal Latin square of order n can be embedded in a diagonal Latin square of order t if and only...
AbstractAn incomplete double diagonal Latin square of order n can be double-diagonally embedded in a...
AbstractWe call a latin square A=(aij) of order n, aij∈{1,2,…,n}, right-diagonal-complete if {(aij,a...
Abstract. A classical question in combinatorics is the following: given a par-tial latin square P, w...
International audienceThe completability of incomplete latin squares can be studied along two lines:...
International audienceThe completability of incomplete latin squares can be studied along two lines:...
International audienceThe completability of incomplete latin squares can be studied along two lines:...
The set PLS(a, b; n) is the set of all partial latin squares of order n with a completed rows, b com...
The set PLS(a, b; n) is the set of all partial latin squares of order n with a completed rows, b com...
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