Skip to main content Accessibility help
×
Home

On the Enumeration of Rooted Non-Separable Planar Maps

  • W. G. Brown (a1) and W. T. Tutte

Extract

It has been shown elsewhere (1, 4) that the number of rooted non-separable planar maps with n edges is

In the present paper we improve upon this result by finding the number fi,j of rooted non-separable planar maps with i + 1 vertices and j + 1 faces. We use the definitions of (1).

Among the non-separable planar maps only the loop-map and the link-map have i = 0 or j = 0. We therefore confine our attention to the case in which i and j are both positive.

    • 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.

      On the Enumeration of Rooted Non-Separable Planar Maps
      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.

      On the Enumeration of Rooted Non-Separable Planar Maps
      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.

      On the Enumeration of Rooted Non-Separable Planar Maps
      Available formats
      ×

Copyright

References

Hide All
1. Brown, W. G., Enumeration of non-separable planar maps, Can. J. Math., 15 (1963), 526 545.
2. Good, I. J., Generalizations to several variables of Lagrange's expansion, with applications to stochastic processes, Proc. Camb. Phil. Soc, 56 (1960), 367380.
3. Goursat, E., A course in mathematical analysis, I and II, Part I (Boston, 1904 and 1916).
4. Tutte, W. T., A census of planar maps, Can. J. Math., 15 (1963), 249271.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

On the Enumeration of Rooted Non-Separable Planar Maps

  • W. G. Brown (a1) and W. T. Tutte

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