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Enumeration of Quadrangular Dissections of the Disk

Published online by Cambridge University Press:  20 November 2018

William G. Brown
William G. Brown*
Affiliation:
University of British Columbia
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A dissection of the disk will be a cell complex (1, p. 39) K with polyhedron the closed disk B2. It will further be required that:

  • (a) every edge of K be incident with two distinct vertices (called its ends) ;

  • (b) no two edges have the same ends ; and

  • (b) no two edges have the same ends ; and

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 17 , 1965 , pp. 302 - 317
Copyright
Copyright © Canadian Mathematical Society 1965

References

1. Ahlfors, L. and Sario, L., Riemann surfaces (Princeton, 1960).Google Scholar
2. Binet, J., Note, J. Math. Pures AppL, 8 (1843), 394–6.Google Scholar
3. Brown, W. G., Enumeration of non-separable planar maps, Can. J. Math., 15 (1963), 528–45.Google Scholar
4. Brown, W. G., Enumeration of triangulations of the disc, Proc. London Math. Soc, (3) 14 (1964), 746–68.Google Scholar
5. Brown, W. G., On the existence of square roots in certain rings of power series, Math. Ann. (to appear).Google Scholar
6. Brown, W. G., Problems in the enumeration of maps, Doctoral thesis (Toronto, 1963).Google Scholar
7. Cayley, A., On the partitions of a polygon, Proc. London Math. Soc. (1st ser.), 22 (1890-91), 237-62.Google Scholar
8. Ethrington, I. H. M. and Erdélyi, A., Some problems of non-associative combinations II, Edinburgh Math. Notes No. 52 (1940), 1–6.Google Scholar
9. Fuss, N., Solutio quaestionis quot modis polygonum n laterum in polygona m laterum per diagonales resolvi queat, Nova Acta Acad. Sci. Imp. Petropolitanae, 9 (1791), 243–51.Google Scholar
10. Grunert, J. A., Uber die Bestimmung der Anzahl der verschiedenen Arten, auf welche sich ein n-eck durch Diagonalen in lauter m-ecke zerlegen lasst, Arch. Math. Phys., Grunert, 1 (1841), 192–203.Google Scholar
11. König, D., Théorie der endlichen und unendlichen Graphen (Leipzig, 1936; reprinted New York, 1950).Google Scholar
12. Liouville, J., Remarques sur un mémoire de N. Fuss, J. Math. Pures AppL, 8 (1843), 391–4.Google Scholar
13. Riordan, J., An introduction to combinatorial analysis (Wiley, 1958).Google Scholar
14. Segner, A., Enumeratio modorum quibus figurae planae rectilineae per diagonales dividuntur in triangula, Novi Comm. Acad. Sci. Imp. Petropolitanae, 7 (1758-59), 203-9.Google Scholar
15. Taylor, H. M. and Rowe, R. C., Note on a geometrical theorem, Proc. London Math. Soc. (1st ser.), 18 (1881-82), 102-6.Google Scholar
16. Tutte, W. T., A census of planar maps, Can. J. Math., 15 (1963), 249–71.Google Scholar
17. Tutte, W. T., A census of planar triangulations, Can. J. Math., 14 (1962), 21–38.Google Scholar
18. Whittaker, E. T. and Watson, G. N., A course of modern analysis (Cambridge, 1927).Google Scholar