## DIMACS TR: 98-01

## Closed Sets and Generators in Ternary Hamming Spaces

### Authors: Endre Boros, Peter L. Hammer, Frederica Ricca and Bruno Simeone

**
ABSTRACT
**

The $n$-dimensional ternary Hamming space is $\TT^n$, where $\TT=\{ 0,
1,2\}$.
Three points in $\TT^n$ form a line if they have in common exactly $n-1$ compone
nts.
A subset of $\TT^n$ 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 $\TT^n$. In this paper, we investigate se
veral properties
of closed sets and generators. Two alternative proofs of our main result,
stating that the minimum cardinality of a generator is $2^n$, are provided.

The present study was motivated by some combinatorial questions concerning
origin-destination matrices in transportation systems.

Paper Available at:
ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1998/98-01.ps.gz

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