Details

Autor(en) / Beteiligte

• Colle, Cleber Fernando

Titel

On periodic decompositions and nonexpansive lines

Ist Teil von

• Mathematische Zeitschrift, 2023-04, Vol.303 (4), Article 80

Ort / Verlag

Berlin/Heidelberg: Springer Berlin Heidelberg

Erscheinungsjahr

2023

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• In his Ph.D. thesis, Michal Szabados conjectured that for a not fully periodic configuration with a minimal periodic decomposition the nonexpansive lines are exactly the lines that contain a period for some periodic configuration in such decomposition. In this paper, we study Szabados’s conjecture. First, we show that we may consider a minimal periodic decomposition where each periodic configuration is defined on a finite alphabet. Then we prove that Szabados’s conjecture holds for a wide class of configurations, which includes all not fully periodic configurations with low convex pattern complexity.