Year: 2012
Type: preprint
Abstract: 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 Gröbner bases, we compute $T(\Z_m \times \Z_n)$ for $2 \leq m \leq 7$ and $2 \leq n \leq 19$.
Source: arXiv (Cornell University)
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1799837307