An infinite sequence of non-realizable weavings

  • Authors:

  • Dušan Repovš;Arkady Skopenkov;Fulvia Spaggiari

  • Affiliations:

  • Institute for Mathematics, Physics and Mechanics, University of Ljubljana, Ljubljana, Slovenia;Department of Differential Geometry, Faculty of Mechanics and Mathematics, Moscow State University, Moscow, Russia;Dipartimento di Matematica, Università degli Studi di Modena e Reggio Emilia, Modena, Italy

  • Venue:
  • Discrete Applied Mathematics - Special issue: Max-algebra
  • Year:
  • 2005

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Abstract

A weaving is a number of lines drawn in the plane so that no three lines intersect at a point, and the intersections are drawn so as to show which of the two lines is above the other. For each integer n ≥ 4 we construct a weaving of n lines, which is not realizable as a projection of a number of lines in 3-space, all of whose subfigures are realizable as such projections.