On the 3-distortion of a path

Authors:
Pierre Dehornoy
Affiliations:
Département de Mathématiques et Applications, ícole Normale Superieure, 45 rue d'Ulm, 75005 Paris, France
Venue:
European Journal of Combinatorics
Year:
2008

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Abstract

We prove that, for embeddings of a path of length n in R^2, the 3-distortion is @W(n^1^/^2), and that, when embedded in R^d, the 3-distortion is O(n^1^/^(^d^-^1^)).