# Enumeration of rooted nonseparable outerplanar maps

Enumeration of rooted nonseparable outerplanar maps In this paper, the number of combinatorially distinct rooted nonseparable outerplanar maps withm edges and the valency of the root-face beingn is found to be $$\frac{{(m - 1)!(m - 2)!}}{{(n - 1)!(n - 2)!(m - n)!(m - n + 1)!}}.$$ And, the number of rooted nonseparable outerplanar maps withm edges is also determined to be $$\frac{{(2m - 2)!}}{{(m - 1)!m!}},$$ which is just the number of distinct rooted plane trees withm − 1 edges. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

# Enumeration of rooted nonseparable outerplanar maps

, Volume 5 (2) – Jul 14, 2005
7 pages

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Publisher
Springer Journals
Copyright © 1989 by Science Press, Beijing, China and Allerton Press, Inc., New York, U.S.A
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/BF02009748
Publisher site
See Article on Publisher Site

### Abstract

In this paper, the number of combinatorially distinct rooted nonseparable outerplanar maps withm edges and the valency of the root-face beingn is found to be $$\frac{{(m - 1)!(m - 2)!}}{{(n - 1)!(n - 2)!(m - n)!(m - n + 1)!}}.$$ And, the number of rooted nonseparable outerplanar maps withm edges is also determined to be $$\frac{{(2m - 2)!}}{{(m - 1)!m!}},$$ which is just the number of distinct rooted plane trees withm − 1 edges.

### Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Jul 14, 2005

### References

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