922 resultados para sums of squares
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Cover title.
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Mode of access: Internet.
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Reprints and detached papers.
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By Moses Beach.
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Mode of access: Internet.
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An announcement by the Committee, dated Feb. 3, 1835, of the planned purchase of more land in Upper Canada for emigrants from the Petworth area: p. [20].
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Mode of access: Internet.
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Mode of access: Internet.
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Mode of access: Internet.
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Mode of access: Internet.
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Mode of access: Internet.
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Mode of access: Internet.
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A critical set in a Latin square of order n is a set of entries from the square which can be embedded in precisely one Latin square of order n, Such that if any element of the critical set. is deleted, the remaining set can be embedded, in more than one Latin square of order n.. In this paper we find all the critical sets of different sizes in the Latin squares of order at most six. We count the number of main and isotopy classes of these critical sets and classify critical sets from the main classes into various strengths. Some observations are made about the relationship between the numbers of classes, particularly in the 6 x 6 case. Finally some examples are given of each type of critical set.
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We find necessary and sufficient conditions for completing an arbitrary 2 by n latin rectangle to an n by n symmetric latin square, for completing an arbitrary 2 by n latin rectangle to an n by n unipotent symmetric latin square, and for completing an arbitrary 1 by n latin rectangle to an n by n idempotent symmetric latin square. Equivalently, we prove necessary and sufficient conditions for the existence of an (n - 1)-edge colouring of K-n (n even), and for an n-edge colouring of K-n (n odd) in which the colours assigned to the edges incident with two vertices are specified in advance.