Results 31 to 40 of about 1,141 (244)
On an asymptotic method in enumeration
Journal of Combinatorial Theory, Series A, 1989 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Amram Meir, John W. Moon
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Asymptotic Enumeration of Labelled Graphs by Genus [PDF]
The Electronic Journal of Combinatorics, 2011 We obtain asymptotic formulas for the number of rooted 2-connected and 3-connected surface maps on an orientable surface of genus $g$ with respect to vertices and edges simultaneously. We also derive the bivariate version of the large face-width result for random 3-connected maps.
Edward A. Bender, Zhicheng Gao
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Degree distribution in random planar graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 We prove that for each $k \geq 0$, the probability that a root vertex in a random planar graph has degree $k$ tends to a computable constant $d_k$, and moreover that $\sum_k d_k =1$. The proof uses the tools developed by Gimènez and Noy in their solution
Michael Drmota, Omer Gimenez, Marc Noy
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Asymptotic Enumeration of Spanning Trees [PDF]
Combinatorics, Probability and Computing, 2005 We give new formulas for the asymptotics of the number of spanning trees of a large graph. A special case answers a question of McKay [Europ. J. Combin. 4 149–160] for regular graphs. The general answer involves a quantity for infinite graphs that we call ‘tree entropy’, which we show is a logarithm of a normalized determinant of the graph Laplacian ...
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Multiple scale asymptotics of map enumeration
Nonlinearity, 2023 Abstract We introduce a systematic approach to express generating functions for the enumeration of maps on surfaces of high genus in terms of a single generating function relevant to planar surfaces. Central to this work is the comparison of two asymptotic expansions obtained from two different fields of mathematics: the Riemann–Hilbert ...
Nicholas Ercolani +2 more
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Enumerating alternating tree families [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 We study two enumeration problems for $\textit{up-down alternating trees}$, i.e., rooted labelled trees $T$, where the labels $ v_1, v_2, v_3, \ldots$ on every path starting at the root of $T$ satisfy $v_1 < v_2 > v_3 < v_4 > \cdots$.
Markus Kuba, Alois Panholzer
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Asymptotics of lattice walks via analytic combinatorics in several variables [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 We consider the enumeration of walks on the two-dimensional non-negative integer lattice with steps defined by a finite set S ⊆ {±1, 0}2 . Up to isomorphism there are 79 unique two-dimensional models to consider, and previous work in this area has used ...
Stephen Melczer, Mark C. Wilson
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Asymptotic Enumeration of Convex Polygons
Journal of Combinatorial Theory, Series A, 1997 A polygon is a self-avoiding cycle in the hypercubic lattice \(\mathbb{Z}^d\) taking at least one step in every dimension. It is convex if its length is exactly twice the sum of the side lengths of the smallest hypercube containing it. An asymptotic expression is given for the number \(p_{n,d}\) of \(d\)-dimensional convex polygons of length \(2n ...
Dudley Stark, Nicholas C. Wormald
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Asymptotic enumeration of Cayley digraphs [PDF]
Israel Journal of Mathematics, 2021 In this paper we show that almost all Cayley digraphs have automorphism group as small as possible; that is, they are digraphical regular representations (DRRs). More precisely, we show that as $r$ tends to infinity, for every finite group $R$ of order $r$, out of all possible Cayley digraphs on $R$ the proportion whose automorphism group is as small ...
Morris J., Spiga P.
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Discrete Mathematics & Theoretical Computer Science, 2007 Let a and b be two positive integers. A culminating path is a path of Z^2 that starts from (0,0), consists of steps (1,a) and (1,-b), stays above the x-axis and ends at the highest ordinate it ever reaches.
Mireille Bousquet-Mélou, Yann Ponty
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