التفاصيل البيبلوغرافية
| العنوان: |
Enumeration of rooted 3-connected bipartite planar maps. |
| المؤلفون: |
Noy, Marc, Requilé, Clément, Rué, Juanjo |
| المصدر: |
Pure Mathematics & Applications; Jun2022, Vol. 30 Issue 1, p97-105, 9p |
| مصطلحات موضوعية: |
BIPARTITE graphs, ALGEBRA, COMBINATORIAL enumeration problems, QUADRATIC equations, POLYNOMIALS |
| مستخلص: |
We provide the first solution to the problem of counting rooted 3-connected bipartite planar maps. Our starting point is the enumeration of bicoloured planar maps according to the number of edges and monochromatic edges, following Bernardi and Bousquet-Mélou [J. Comb. Theory Ser. B (2011)]. The decomposition of a map into 2- and 3-connected components allows us to obtain the generating functions of 2- and 3-connected bicoloured maps. Setting to zero the variable marking monochromatic edges we obtain the generating function of 3-connected bipartite maps, which is algebraic of degree 26. We deduce from it an asymptotic estimate for the number of 3-connected bipartite planar maps of the form t · n−5/2γn, where γ = ρ−1 ≈ 2.40958 and ρ ≈ 0.41501 is an algebraic number of degree 10. [ABSTRACT FROM AUTHOR] |
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| قاعدة البيانات: |
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