منابع مشابه
Latin Squares with Forbidden Entries
An n× n array is avoidable if there exists a Latin square which differs from the array in every cell. The main aim of this paper is to present a generalization of a result of Chetwynd and Rhodes involving avoiding arrays with multiple entries in each cell. They proved a result regarding arrays with at most two entries in each cell, and we generalize their method to obtain a similar result for a...
متن کاملMaximal Partial Latin Cubes
We prove that each maximal partial Latin cube must have more than 29.289% of its cells filled and show by construction that this is a nearly tight bound. We also prove upper and lower bounds on the number of cells containing a fixed symbol in maximal partial Latin cubes and hypercubes, and we use these bounds to determine for small orders n the numbers k for which there exists a maximal partial...
متن کاملSome partial Latin cubes and their completions
It iswell known that all n×n partial Latin squareswith atmost n−1 entries are completable. Our intent is to extend this well known statement to partial Latin cubes.We show that if an n×n×n partial Latin cube contains at most n − 1 entries, no two of which occupy the same row, then the partial Latin cube is completable. Also included in this paper is the problem of completing 2×n×n partial Latin...
متن کاملLatin Cubes and Hypercubes of Prime Order
In [3]s the first author obtained an expression for the number of equivalence classes induced on the set of ft x ft Latin squares under row and column permutations. The first purpose of this paper is to point out that the results of [3] do not hold for all n, but rather that they hold only if n is a prime.* The second purpose of this paper is, in the case of prime ft, to extend the results of [...
متن کاملWireless Network-Coded Multi-Way Relaying Using Latin Hyper-Cubes
Physical layer network-coding for the n-way wireless relaying scenario is dealt with, where each of the n user nodes X1, X2, ..., Xn wishes to communicate its messages to all the other (n−1) nodes with the help of the relay node R. The given scheme, based on the denoise-and-forward scheme proposed for two-way relaying by Popovski et al. in [1], employs two phases: Multiple Access (MA) phase and...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2019
ISSN: 1077-8926
DOI: 10.37236/8157