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Analysis and Geometry in Metric Spaces

Ed. by Ritoré, Manuel

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CiteScore 2017: 0.65

SCImago Journal Rank (SJR) 2017: 1.063
Source Normalized Impact per Paper (SNIP) 2017: 0.833

Mathematical Citation Quotient (MCQ) 2016: 0.78


Emerging Science

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Online
ISSN
2299-3274
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Constant Distortion Embeddings of Symmetric Diversities

David Bryant
  • Corresponding author
  • Dept. of Mathematics, Simon Fraser University. 8888 University Drive, Burnaby, British Columbia V5A 1S6, Canada,
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Paul F. Tupper
  • Corresponding author
  • Dept. of Mathematics and Statistics, University of Otago, Dunedin 9054, New Zealand
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2016-12-05 | DOI: https://doi.org/10.1515/agms-2016-0016

Abstract

Diversities are like metric spaces, except that every finite subset, instead of just every pair of points, is assigned a value. Just as there is a theory of minimal distortion embeddings of fiite metric spaces into L1, there is a similar, yet undeveloped, theory for embedding finite diversities into the diversity analogue of L1 spaces. In the metric case, it iswell known that an n-point metric space can be embedded into L1 withO(log n) distortion. For diversities, the optimal distortion is unknown. Here, we establish the surprising result that symmetric diversities, those in which the diversity (value) assigned to a set depends only on its cardinality, can be embedded in L1 with constant distortion.

Keywords: diversities; metric embedding; L1 embedding; hypergraphs

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About the article

Received: 2016-05-11

Accepted: 2016-11-08

Published Online: 2016-12-05


Citation Information: Analysis and Geometry in Metric Spaces, Volume 4, Issue 1, ISSN (Online) 2299-3274, DOI: https://doi.org/10.1515/agms-2016-0016.

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© 2016 David Bryant and Paul F. Tupper. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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