Submap Density and Asymmetry Results for Two Parameter Map Families

Combinatorics Probability and Computing

Volumn 6, Issue 1, 1997, Pages 17-25

  Bender, Edward A ^a   Canfield, E Rodney ^b   Gao, Zhicheng ^c   Ricmond, L Bruce ^d  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b University of Georgia ^*  (United States)

^c CARLETON UNIVERSITY   (Canada)

^d UNIVERSITY OF WATERLOO   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031541205     PISSN: 09635483     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0963548396002799     Document Type: Article

References (15)

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2. Bender, E. A., Canfield, E. R. and Richmond, L. B. (1993) The asymptotic number of rooted maps on a surface. II: Enumeration by vertices and faces. J. Combin. Theory, Ser. A 63 318-329.
3. Bender, E. A., Gao, Z. C. and Richmond, L. B. (1992) Submaps of maps. I: General 0-1 laws. J. Combin. Theory, Ser. B 55 104-117.
4. Bender, E. A., Gao, Z. C., McCuaig, W. D. and Richmond, L. B. (1992) Submaps of maps. II: Cyclically k-connected planar cubic maps. J. Combin. Theory, Ser. B 55 118-124.
5. Bender, E. A. and Richmond, L. B. (1992) Submaps of maps. III: k-connected nonplanar maps. J. Combin. Theory, Ser. B 55 125-132.
6. Bender, E. A., Richmond, L. B. and Wormald, N. C. (1993) Submaps of maps. IV: Degree restricted nonplanar maps. Ars Combinatorial 35-A 135-142.
7. Bender, E. A. and Richmond, L. B. (1983) Central and local limit theorems applied to asymptotic enumeration. II: Multivariate generating functions. J. Combin. Theory, Ser. A 34 255-265.
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9. Bender, E. A. and Wormald, N. C. (1985) Almost all convex polyhedra are asymmetric. Canad. J. Math. 27 854-871.
10. Bender, E. A. and Wormald, N. C. (1988) The asymptotic number of rooted nonseparable maps on a surface. J. Combin. Theory, Ser. A 49 370-380.
11. Brown, W. G. and Tutte, W. T. (1964) On the enumeration of rooted non-separable planar maps. Canad. J. Math. 16 572-577.
12. Meir, A. and Moon, J. W. (1989) On an asymptotic method in enumeration. J. Combin. Theory, Ser. A 51 77-89.
13. Richmond, L. B. and Wormald, N. C. (1995) Almost all maps are asymmetric. J. Combin. Theory, Ser. B 63 1-7.
14. Szegö, G. (1959) Orthogonal Polynomials, Amer. Math. Soc. Coll. Publ., vol. XXIII, rev. ed., Amer. Math. Soc., New York.
15. Tutte, W. T (1962) A census of slicings. Canad. J. Math. 14 708-722.