共查询到20条相似文献,搜索用时 31 毫秒
1.
Zhaoxiang Li 《Discrete Mathematics》2007,307(1):78-87
In this paper, we study the chromatic sum functions of rooted general maps on the sphere and the projective plane. The chromatic sum function equations of such maps are obtained. From the chromatic sum equations of such maps, the enumerating function equations of rooted loopless maps, bipartite maps and Eulerian maps are also derived. Moreover, some explicit expressions of enumerating functions are also derived. 相似文献
2.
In this paper, boundary cubic rooted planar maps are investigated and exact enumerative formulae are given. First, an enumerative formula for boundary cubic inner-forest maps with the size (number of edges) as a parameter is derived. For the special case of boundary cubic inner-tree maps, a simple formula with two parameters is presented. Further, according to the duality, a corresponding result for outer-planar maps is obtained. Finally, some results for boundary cubic planar maps and general planar maps are obtained. Furthermore, two known Tutte's formulae are easily deduced in the paper. 相似文献
3.
Song Jiang 《Annali di Matematica Pura ed Applicata》1998,175(1):253-275
We study Lagrangian systems with symmetry under the action of a constant generalized force in the direction of the symmetry field. After Routh's reduction, such systems become nonautonomous with Lagrangian quadratic in time. We prove the existence of solutions tending to an orbit of the symmetry group as t± . As an example, we study doubly asymptotic solutions for the Kirchhoff problem of a heavy rigid body in an infinite volume of incompressible ideal fluid performing a potential motion.Supported by GNFM and by MURST (40%: «Equazioni di evoluzione...»).Supported by Russian Foundation of Basic Research and by INTAS. 相似文献
4.
We introduce a new approach to the study of affine equidistants and centre symmetry sets via a family of maps obtained by reflexion in the midpoints of chords of a submanifold of affine space. We apply this to surfaces in R3, previously studied by Giblin and Zakalyukin, and then apply the same ideas to surfaces in R4, elucidating some of the connexions between their geometry and the family of reflexion maps. We also point out some connexions with symplectic topology. 相似文献
5.
Olivier Bernardi 《Advances in Applied Mathematics》2012,48(1):164-180
A unicellular map is the embedding of a connected graph in a surface in such a way that the complement of the graph is simply connected. In a famous article, Harer and Zagier established a formula for the generating function of unicellular maps counted according to the number of vertices and edges. The keystone of their approach is a counting formula for unicellular maps on orientable surfaces with n edges, and with vertices colored using every color in [q] (adjacent vertices are authorized to have the same color). We give an analogue of this formula for general (locally orientable) surfaces.Our approach is bijective and is inspired by Lass?s proof of the Harer-Zagier formula. We first revisit Lass?s proof and twist it into a bijection between unicellular maps on orientable surfaces with vertices colored using every color in [q], and maps with vertex set [q] on orientable surfaces with a marked spanning tree. The bijection immediately implies Harer-Zagier?s formula and a formula by Jackson concerning bipartite unicellular maps. It also shed a new light on constructions by Goulden and Nica, Schaeffer and Vassilieva, and Morales and Vassilieva. We then extend the bijection to general surfaces and obtain a correspondence between unicellular maps on general surfaces with vertices colored using every color in [q], and maps on orientable surfaces with vertex set [q]with a marked planar submap. This correspondence gives an analogue of the Harer-Zagier formula for general surfaces. We also show that this formula implies a recursion formula due to Ledoux for the numbers of unicellular maps with given numbers of vertices and edges. 相似文献
6.
We attempt a broad exploration of properties and connections between the symmetry function of a convex set S ${S \subset\mathbb{R}^n}We attempt a broad exploration of properties and connections between the symmetry function of a convex set S
and other arenas of convexity including convex functions, convex geometry, probability theory on convex sets, and computational
complexity. Given a point , let sym(x,S) denote the symmetry value of x in S:
, which essentially measures how symmetric S is about the point x, and define
x
* is called a symmetry point of S if x
* achieves the above maximum. The set S is a symmetric set if sym
(S)=1. There are many important properties of symmetric convex sets; herein we explore how these properties extend as a function
of sym
(S) and/or sym
(x,S). By accounting for the role of the symmetry function, we reduce the dependence of many mathematical results on the strong
assumption that S is symmetric, and we are able to capture and otherwise quantify many of the ways that the symmetry function influences properties
of convex sets and functions. The results in this paper include functional properties of sym
(x,S), relations with several convex geometry quantities such as volume, distance, and cross-ratio distance, as well as set approximation
results, including a refinement of the L?wner-John rounding theorems, and applications of symmetry to probability theory on
convex sets. We provide a characterization of symmetry points x
* for general convex sets. Finally, in the polyhedral case, we show how to efficiently compute sym(S) and a symmetry point x
* using linear programming. The paper also contains discussions of open questions as well as unproved conjectures regarding
the symmetry function and its connection to other areas of convexity theory.
Dedicated to Clovis Gonzaga on the occasion of his 60th birthday. 相似文献
7.
We show that the maximum vertex degree in a random
3-connected planar triangulation is concentrated in an interval
of almost constant width. This is a slightly weaker type of
result than our earlier determination of the limiting
distribution of the maximum vertex degree in random planar maps
and in random triangulations of a (convex) polygon. We also
derive sharp concentration results on the number of vertices of
given degree in random planar maps of all three types. Some
sharp concentration results about general submaps in 3-connected
triangulations are also given.* Research supported by NSERC and Australian
Research Council Research supported by the Australian Research
Council 相似文献
8.
We compute the number of rhombus tilings of a hexagon with sidesN,M,N, N,M,N, which contain a fixed rhombus on the symmetry axis that cuts through the sides of lengthM. 相似文献
9.
RenHan LiuYanpei 《高校应用数学学报(英文版)》1999,14(1):117-121
A Halin map is a kind of planar maps oriented by a tree. In this paper the rooted halin maps with the vertex partition as parameters are enumerated such that a famous result on rooted trees due to Harary. Prins, and Tutte is deduced as. a special ease. Further, by using Lagrangian inversion to obtain a number of summation free formulae dixectly, the various kinds of rooted Halin maps with up to three parameters have been counted. 相似文献
10.
It is well known that regular maps exist on the projective plane but not on the Klein bottle, nor the non-orientable surface of genus 3. In this paper several infinite families of regular maps are constructed to show that such maps exist on non-orientable surfaces of over 77 per cent of all possible genera. 相似文献
11.
F. Comellas 《Linear algebra and its applications》2008,429(7):1823-1839
The multidimensional Manhattan street networks constitute a family of digraphs with many interesting properties, such as vertex symmetry (in fact they are Cayley digraphs), easy routing, Hamiltonicity, and modular structure. From the known structural properties of these digraphs, we determine their spectra, which always contain the spectra of hypercubes. In particular, in the standard (two-dimensional) case it is shown that their line digraph structure imposes the presence of the zero eigenvalue with a large multiplicity. 相似文献
12.
A plane graph is called symmetric if it is invariant under the reflection across some straight line (called symmetry axis). Let G be a symmetric plane graph. We prove that if there is no edge in G intersected by its symmetry axis then the number of spanning trees of G can be expressed in terms of the product of the number of spanning trees of two smaller graphs, each of which has about half the number of vertices of G. 相似文献
13.
Aarno Hohti 《Topology and its Applications》2009,156(7):1371-1373
We consider choice functions k[X]→X, where X is a finite set and k[X] denotes the set of all k-subsets of X. We define a property of domination for such maps generalizing the classical case k=2 (tournaments) and prove the existence of a dominating element generalizing the existence of a 2-root (king) in the classical case. 相似文献
14.
Jonathan David Farley 《Order》1995,12(1):5-44
We compute the number of order-preserving and -reversing maps between posets in the class of fences (zig-zags) and crowns (cycles). 相似文献
15.
Combinatorica - Quadratic programming, symmetry, positive (semi) definiteness and the linear complementary problem were generalized by Morris and Todd to oriented matroids. Todd gave a constructive... 相似文献
16.
David E. Evans 《Acta Appl Math》1984,2(3-4):333-352
A survey of the recent work on the infinitesimal generators of one-parameter semigroups of positivity preserving maps on operator algebras, in the presence of compact symmetry groups or flows. 相似文献
17.
18.
Gopala Krishna Srinivasan 《Expositiones Mathematicae》2013,31(2):151-168
In this paper, we provide a unified approach to a family of integrals of Mellin–Barnes type using distribution theory and Fourier transforms. Interesting features arise in many of the cases which call for the application of pull-backs of distributions via smooth submersive maps defined by Hörmander. We derive by this method the integrals of Hecke and Sonine related to various types of Bessel functions which have found applications in analytic and algebraic number theory. 相似文献
19.
Given an n-vertex graph G=(V,E), the Laplacian spectrum of G is the set of eigenvalues of the Laplacian matrix L=D-A, where D and A denote the diagonal matrix of vertex-degrees and the adjacency matrix of G, respectively. In this paper, we study the Laplacian spectrum of trees. More precisely, we find a new upper bound on the sum of the k largest Laplacian eigenvalues of every n-vertex tree, where k∈{1,…,n}. This result is used to establish that the n-vertex star has the highest Laplacian energy over all n-vertex trees, which answers affirmatively to a question raised by Radenkovi? and Gutman [10]. 相似文献
20.
An upper bound is given on the number of acyclic orientations of a graph, in terms of the spectrum of its Laplacian. It is shown that this improves upon the previously known bound, which depended on the degree sequence of the graph. Estimates on the new bound are provided.A lower bound on the number of acyclic orientations of a graph is given, with the help of the probabilistic method. This argument can take advantage of structural properties of the graph: it is shown how to obtain stronger bounds for small-degree graphs of girth at least five, than are possible for arbitrary graphs. A simpler proof of the known lower bound for arbitrary graphs is also obtained.Both the upper and lower bounds are shown to extend to the general problem of bounding the chromatic polynomial from above and below along the negative real axis.Partially supported by the NSF under grant CCR-9404113. Most of this research was done while the author was at the Massachusetts Institute of Technology, and was supported by the Defense Advanced Research Projects Agency under Contracts N00014-92-J-1799 and N00014-91-J-1698, the Air Force under Contract F49620-92-J-0125, and the Army under Contract DAAL-03-86-K-0171.Supported by an ONR graduate fellowship, grants NSF 8912586 CCR and AFOSR 89-0271, and an NSF postdoctoral fellowship. 相似文献