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2 results

  • Some Remarks on Translative Coverings of Convex Domains by Strips

  • H. Groemer
  • Journal:
    Canadian Mathematical Bulletin / Volume 27 / Issue 2 / 01 June 1984
    Published online by Cambridge University Press:
    20 November 2018, pp. 233-237
    Print publication:
    01 June 1984
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  • In the euclidean plane let K be a compact convex set and Sl, S2,… strips of respective widths wl, w2,… Some conditions on Σ wi are given that imply that K can be covered by translates of the strips Si. These conditions involve the perimeter, the diameter, or the minimal width of K and yield improvements of previously known results.

  • Hausdorff Obstructions to Packing (N-1)-Balls in N-Space

  • J. B. Wilker
  • Journal:
    Canadian Mathematical Bulletin / Volume 25 / Issue 4 / 01 December 1982
    Published online by Cambridge University Press:
    20 November 2018, pp. 414-420
    Print publication:
    01 December 1982
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  • An arbitrary collection of (N — l)-flats in ℝN is called a frame and an arbitrary assignment of (N — 1))-balls to these (N — 1)-flats is called a loading. Any loading in which the designated (N — 1)-balls are mutually disjoint is called a packing. For the frame consisting of the (N — 1)-flats perpendicular to a given line, every loading is automatically a packing. Although this is obviously not the most general frame to admit a packing, we show two senses in which all frames which admit packings are "at most onedimensional." Our principal tool is the Hausdorff measure-theoretic dimension.