منابع مشابه
Transversals in Rectangles
Let L(m;n) be the largest integer such that, if each symbol in an m n rectangle occurs at most L(m;n) times, then the array must have a transversal. We improve the lower bound to L(m;n) b m+1) 1 m 1 c, form > 1. Then we show that sporadically L(m;n) < bmn 1 m 1 c in the range m n m 3m + 3. De ne n0(m) to be the smallest integer z such that if n z then L(m;n) = bmn 1 m 1 c. We improve n0(m) from...
متن کاملA Matroid Generalization of a Result on Row-Latin Rectangles
Let A be an m n matrix in which the entries of each row are all distinct. Drisko 4] showed that, if m 2n ? 1, then A has a transversal: a set of n distinct entries with no two in the same row or column. We generalize this to matrices with entries in a matroid. For such a matrix A, we show that if each row of A forms an independent set, then we can require the transversal to be independent as we...
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...
متن کاملAdditive Latin Transversals
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 generalized Latin squares
We are seeking a sufficient condition that forces a transversal in a generalized Latin square. A generalized Latin square of order n is equivalent to a proper edge-coloring of Kn,n. A transversal corresponds to a multicolored perfect matching. Akbari and Alipour defined l(n) as the least integer such that every properly edge-colored Kn,n, which contains at least l(n) different colors, admits a ...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1998
ISSN: 0097-3165
DOI: 10.1006/jcta.1998.2894