The Euclidean Distortion of the Lamplighter Group
نویسندگان
چکیده
We show that the cyclic lamplighter group C2 oCn embeds into Hilbert space with distortion O ( √ log n ) . This matches the lower bound proved by Lee, Naor and Peres in [14], answering a question posed in that paper. Thus the Euclidean distortion of C2 o Cn is Θ ( √ log n ) . Our embedding is constructed explicitly in terms of the irreducible representations of the group. Since the optimal Euclidean embedding of a finite group can always be chosen to be equivariant, as shown by Aharoni, Maurey and Mityagin [1] and by Gromov (see [9]), such representation-theoretic considerations suggest a general tool for obtaining upper and lower bounds on Euclidean embeddings of finite groups.
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ورودعنوان ژورنال:
- Discrete & Computational Geometry
دوره 44 شماره
صفحات -
تاریخ انتشار 2010