Translative covering of a square by a sequence of arbitrary-oriented squares

• Autorzy: Januszewski J.
• Języki publikacji: EN

Abstrakty

EN

Given a collection of squares in the plane whose side lengths are not larger than 1 and whose total area is at least 3. Then the unit square can be covered by translates of these squares.

Słowa kluczowe

EN

covering transformation; sequences; covering theorems; convex geometry

PL

odwzorowania nakrywające; ciągi; twierdzenie o pokryciu; geometria całkowa

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2007
• Tom: Vol. 40, nr 3
• Strony: 681--700
• Opis fizyczny: Bibliogr. 5 poz.

Twórcy

autor

Januszewski J.

• Institute of Mathematics and Physics University of Technology and Natural Sciences, ul. Kaliskiego 7, 85-796 Bydgoszcz, Poland,

Bibliografia

• [1] G. Fejes Tóth and W. Kuperberg, Packing and Covering with Convex Sets, in: Handbook of Convex Geometry, Vol. B, North-Holland, Amsterdam, 1993, 799-860.
• [2] H. Groemer, Covering and packing by sequences of convex bodies, in: Discrete Geometry and Convexity, Ann. New York Acad. Sci., Vol. 440 (1985), 262-278.
• [3] J. Januszewski, Covering the unit square by squares, Beitr. Algebra Geom. 43 (2) (2002), 411-422.
• [4] J. W. Moon and L. Moser, Some packing and covering theorems, Colloq. Math. 17 (1967), 103-110.
• [5] W. Moser and J. Pach, Research problems in discrete geometry, Privately published collection of problems, 1994.