Skip to main content Accessibility help
×
Home

A generalization of Radon's theorem II

  • H. Tverberg (a1)

Abstract

A new proof is given of the following result: Let m and d be positive integers, and let a set of md + md points be given in d-dimensional space. Then the set can be partitioned into m sets such that the m convex polytopes spanned by the sets have a non-empty intersection.

    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      A generalization of Radon's theorem II
      Available formats
      ×

      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      A generalization of Radon's theorem II
      Available formats
      ×

      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      A generalization of Radon's theorem II
      Available formats
      ×

Copyright

References

Hide All
[1]Bárány, Imre, “A generalization of Carathéodory's theorem”, preprint.
[2]Doignon, J.-P. and Valette, G., “Radon partitions and a new notion of independence in affine and projective spaces”, Mathematika 24 (1977), 8696.
[3]Eckhoff, Jürgen, “Radon's theorem revisited”, Contributions to geometry, 164185 (Proc. Geom. Sympos., Siegen, 1978. Birkhäuser, Basel, 1979).
[4]Reay, John R., “An extension of Radon's theorem”, Illinois J. Math. 12 (1968) 184189.
[5]Reay, J., “Open problems around Radon's theorem”, Proceedings of the J. Clarence Karcher conference on convexity and related combinatorics (Marcel Dekker, to appear).
[6]Tverberg, H., “A generalization of Radon's theorem”, J. London Math. Soc. 41 (1966), 123128.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed