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We study the orthogonal projections of a large class of self-affine carpets, which contains the carpets of Bedford and McMullen as special cases. Our main result is that if Λ is such a carpet, and certain natural irrationality conditions hold, then every orthogonal projection of Λ in a non-principal direction has Hausdorff dimension min(γ,1), where γ is the Hausdorff dimension of Λ. This generalizes a recent result of Peres and Shmerkin on sums of Cantor sets.
School of Mathematics, and Centre for Interdisciplinary Computational, and Dynamical Analysis, Alan Turing Building, University of Manchester, Oxford Road, Manchester M13 9PL, UK