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Projecting the onedimensional Sierpinski gasket
 Richard Kenyon
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LetS⊂ℝ^{2} be the Cantor set consisting of points (x,y) which have an expansion in negative powers of 3 using digits {(0,0), (1,0), (0,1)}. We show that the projection ofS in any irrational direction has Lebesgue measure 0. The projection in a rational directionp/q has Hausdorff dimension less than 1 unlessp+q ≡ 0 mod 3, in which case the projection has nonempty interior and measure 1/q. We compute bounds on the dimension of the projection for certain sequences of rational directions, and exhibit a residual set of directions for which the projection has dimension 1.
This work was partially completed while the author was at the Institut Fourier, Grenoble, France.
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 Title
 Projecting the onedimensional Sierpinski gasket
 Journal

Israel Journal of Mathematics
Volume 97, Issue 1 , pp 221238
 Cover Date
 19971201
 DOI
 10.1007/BF02774038
 Print ISSN
 00212172
 Online ISSN
 15658511
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Industry Sectors
 Authors

 Richard Kenyon ^{(1)}
 Author Affiliations

 1. CNRS UMR 128, Ecole Normale Superieure de Lyon, 46, allée d’Italie, 69364, Lyon, France