Covering with latin transversals
نویسندگان
چکیده
منابع مشابه
Latin Squares with No Transversals
A k-plex in a latin square of order n is a selection of kn entries that includes k representatives from each row and column and k occurrences of each symbol. A 1-plex is also known as a transversal. It is well known that if n is even then Bn, the addition table for the integers modulo n, possesses no transversals. We show that there are a great many latin squares that are similar to Bn and have...
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 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 کاملTransversals of Additive Latin Squares
Let A = {a1, . . . , ak} and B = {b1, . . . , bk} be two subsets of an Abelian group G, k ≤ |G|. Snevily conjectured that, when G is of odd order, there is a permutation π ∈ Sk such that the sums ai+bπ(i), 1 ≤ i ≤ k, are pairwise different. Alon showed that the conjecture is true for groups of prime order, even when A is a sequence of k < |G| elements, i.e., by allowing repeated elements in A. ...
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 ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 1995
ISSN: 0166-218X
DOI: 10.1016/0166-218x(93)e0136-m