Naslov
Combinatorial settlement planning

Autori
Puljiz, Mate ; Šebek, Stjepan ; Žubrinić, Josip

Vrsta, podvrsta
Radovi u časopisima, znanstveni

Izvornik
Contributions to Discrete Mathematics (2023)

Status rada
Prihvaćen

Ključne riječi
maximal configuration ; optimal patterns ; tilings ; forbidden induced subgraph problem ; shift space

Sažetak
In this article, we consider a combinatorial settlement model on a rectangular grid where at least one side (east, south or west) of each house must be exposed to sunlight without obstructions. We are interested in maximal configurations, where no additional houses can be added. For a fixed m×n grid we explicitly calculate the lowest number of houses, and give close to optimal bounds on the highest number of houses that a maximal configuration can have. Additionally, we provide an integer programming formulation of the problem and solve it explicitly for small values of m and n.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA