Translative covering by unit squares

• Autorzy: Januszewski J.
• Języki publikacji: EN

Abstrakty

EN

Some results concerning translative coverings of squares and triangles by two, three and four unit squares are presented.

Słowa kluczowe

EN

covering; square; triangle

PL

pokrycia; kwadrat; trójkąt

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2013
• Tom: Vol. 46, nr 3
• Strony: 605--616
• Opis fizyczny: Bibliogr. 12 poz., rys., tab.

Twórcy

autor

Januszewski J.

• Institute of Mathematics and Physics, University of Technology and Life Sciences, Kaliskiego 7, 85-789 Bydgoszcz, Poland

Bibliografia

• [1] K. Böröczky, Jr., Finite packing and covering, Cambridge Tracts in Mathematics, 154, Cambridge University Press, Cambridge, 2004.
• [2] P. Brass, W. Moser, J. Pach, Research Problems in Discrete Geometry, Springer, New York, 2005.
• [3] G. Fejes Tóth, W. Kuperberg, Packing and covering with convex sets, in: Handbook of Convex Geometry, P. M. Gruber, J. M. Wills, eds., North-Holland, 1993, 799–860.
• [4] E. Friedman, http://www2.stetson.edu/efriedma/packing.html
• [5] F. Göbel, Geometrical packing and covering problems, in: Packing and Covering in Combinatorics, A. Schrijver, ed., Math. Centrum Tracts 106 (1979), 179–199.
• [6] H. Groemer, Covering and packing properties of bounded sequences of convex sets, Mathematika 29 (1982), 18–31.
• [7] E. Hlawka, Ausfüllung und Überdeckung konvexer Körper durch konvexe Körper, Monatsch. Math. 53 (1949), 81–131.
• [8] J. Januszewski, Covering the unit square by squares, Beiträge Algebra. Geom. 43(2) (2002), 411–422.
• [9] J. Januszewski, Translative covering of a square by a sequence of arbitrary-oriented squares, Demonstratio Math. 40(3) (2007), 681–700.
• [10] J. W. Moon, L. Moser, Some packing and covering theorems, Colloq. Math. 17 (1967), 103–110.
• [11] W. Moser, J. Pach, Research problems in discrete geometry, Privetly published collection of problems, 1994.
• [12] A. Soifer, Covering a square of side n+ϵ with unit squares, J. Combin. Theory Ser. A 113 (2006), 380–383.