Closed Sets and Generators in Ternary Hamming Spaces 1
نویسندگان
چکیده
The n-dimensional ternary Hamming space is Tn, where T = f0; 1; 2g. Three points in Tn form a line if they have in common excactly n 1 components. A subset of Tn is closed if, whenever it contains two points of a line, it contains also the third one. A generator is a set, whose closure is Tn. In this paper, we investigate several properties of closed sets and generators. Two alternative proofs of our main result, stating that the minimum cardinality of a generator is 2n, are provided. The present study was motivated by some combinatorial questions concerning origin-destination matrices in transportation systems.
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