The no-three-in-line problem on a torus

Details The no-three-in-line problem on a torus The no-three-in-line problem on a torus

2012-03-29

arxiv.org/abs/1203.6604v1

Mathematics

Combinatorics

10 pages, 3 figures

Scientific paper

Let $T(\Z_m \times \Z_n)$ denote the maximal number of points that can be placed on an $m \times n$ discrete torus with "no three in a line," meaning no three in a coset of a cyclic subgroup of $\Z_m \times \Z_n$. By proving upper bounds and providing explicit constructions, for distinct primes $p$ and $q$, we show that $T(\Z_p \times \Z_{p^2}) = 2p$ and $T(\Z_p \times \Z_{pq}) = p+1$. Via Gr\"obner bases, we compute $T(\Z_m \times \Z_n)$ for $2 \leq m \leq 7$ and $2 \leq n \leq 19$.

Affiliated with

Also associated with

No associations

Rating

The no-three-in-line problem on a torus does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The no-three-in-line problem on a torus, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The no-three-in-line problem on a torus will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-58352