A complete census of convex lattice polygons with one interior lattice point

• Autorzy: Olszewska D.
• Konferencja: II Konferencja dla Młodych Matematyków. Zastosowania Matematyki -Lądek Zdrój 2001
• Języki publikacji: EN

Abstrakty

EN

In 1980 Arkinstall [1] proved that (up to lattice equivalence - defined below) there is just one convex lattice hexagon containing a single interior lattice point. Looking for a census of all convex lattice polygons with one interior lattice point Rabinowitz [2] obtained fifteen classes of equivalent polygons. Somehow he omitted one class of such polygons. The purpose of this note is to show that a complete census of convex lattice polygons with one interior lattice point in fact consists of sixteen classes of equivalent polygons.

• Wydawca: Oficyna Wydawnicza Politechniki Wrocławskiej
• Czasopismo: Prace Naukowe Instytutu Matematyki Politechniki Wrocławskiej. Konferencje
• Rocznik: 2003
• Tom: Vol. 25, nr 4
• Strony: 57--61
• Opis fizyczny: Bibliogr. 3 poz.

Twórcy

autor

Olszewska D.

• Institute of Mathematics, Wrocław University of Technoloy, Poland.

Bibliografia

• [1] J. R. Arkinstall, Minimal Requirements for Minkowski's Theorem int the Plane /, Bull. Austral. Math. Soc. 22 (1980), 259-274.
• [2] S. Rabinowitz, A census of convex lattice polygons with at most one interior lattice point, Ars Com bin. 28 (1989), 83-96.
• [3] P. R. Scott, The fascination of the elementary, Amer. Math. Monthly, 94 (1987), 75-9-768.