On completing three cyclically generated transversals to a latin square
نویسندگان
چکیده
منابع مشابه
The number of transversals in a Latin square
A Latin square of order n is an n × n array of n symbols, in which each symbol occurs exactly once in each row and column. A transversal is a set of n entries, one selected from each row and each column of a Latin square of order n such that no two entries contain the same symbol. Define T (n) to be the maximum number of transversals over all Latin squares of order n. We show that bn ≤ T (n) ≤ ...
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We give a condition on the spatial distribution of filled cells in a partial Latin square P that is sufficient to ensure completability, regardless of what symbols are used in the filled cells. For example, if P is of the order mr + t, where m, r are positive integers and t ≥ 0, m is odd, and the filled cells of P are contained in the first m+1 2 r × r subsquares along the main diagonal, our co...
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We prove that for every odd prime p, every k ≤ p and every two subsets A = {a1, . . . , ak} and B = {b1, . . . , bk} of cardinality k each of Zp, there is a permutation π ∈ Sk such that the sums ai + bπ(i) (in Zp) are pairwise distinct. This partially settles a question of Snevily. The proof is algebraic, and implies several related results as well.
متن کاملTransversals in Latin Squares
A latin square of order n is an n×n array of n symbols in which each symbol occurs exactly once in each row and column. A transversal of such a square is a set of n entries such that no two entries share the same row, column or symbol. Transversals are closely related to the notions of complete mappings and orthomorphisms in (quasi)groups, and are fundamental to the concept of mutually orthogon...
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ژورنال
عنوان ژورنال: Finite Fields and Their Applications
سال: 2009
ISSN: 1071-5797
DOI: 10.1016/j.ffa.2008.05.009