共查询到19条相似文献,搜索用时 609 毫秒
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自20世纪60年代初Tutte的开创性工作以来,许多学者在带根地图的计数方面作了很多工作,但许多类无环地图的计数仍没有被处理.本文主要研究以根点次、非根点数和内面数为三个参数的带根无环欧拉平面地图的计数问题. 相似文献
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近三正则3—连通平面地图的计数 总被引:2,自引:0,他引:2
本文提供了便于依根点次,边数和根面次计数近三正则3-连通有根平面地图的一个函数方程,继之得到其参数形式解,并由此通过Lagrange反演导出了它的计数显示,本文推广了[3]和[4]的结果。 相似文献
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有根不可分离平面偶地图的计数 总被引:3,自引:0,他引:3
刘彦佩 《数学物理学报(A辑)》1989,9(1):21-28
本文给出了由边数和根面的次作为指标的有根不可分离平面偶地图的计数函数所满足的函效方程,此方程是三次的。而,有根一般平面偶地图的相应计数函数所满足的方程却是二次的。从此后一个方程出发得到了上面提到的二个计数函数的具体形式。同时,发现了这个有根不可分离平面偶地图的计数函数与Fabonacci叙列的关系。 相似文献
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环面上一般有根地图的计数 总被引:1,自引:0,他引:1
这篇文章给出了环面上以内面个数,根面次和非根节点个数为参数的一般有根地图的计数方程,导出了以内面个数和非根节点个数为参数的这类地图的计数方程的精确解。作为推论,推出了以边数为参数的这类地图的个数,其近似解在文献[2]中已讨论。 相似文献
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本文研究了Euler方程φ(x)=k的解,我们用Selberg筛法证明了下述定理,设m,k是任意的正整数,则使方程mp^k=φ(y)有解的不超过x的素数p的个数为O(x/log^2x)。 相似文献
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本文讨论了带根双奇异平面地图的计数问题,提供了以根面次、度和内面数为参数及以根面次、奇异边数和自环数为参数的计数函数所满足的计数方程,并且导出了所有的计数显式. 相似文献
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将Lehmer同余式从模素数的平方推广到模任意整数的平方,王容、廖群英定义了一类正整数n广义欧拉函数φn (5),并给出了准确计算公式,利用已有的广义欧拉函数计算公式,使用初等的方法和技巧,研究了一类广义欧拉函数方程φ5(n)=n/d的正整数解. 相似文献
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《Discrete Mathematics》2022,345(9):112975
Universal cycle for k-permutations is a cyclic arrangement in which each k-permutation appears exactly once as k consecutive elements. Enumeration problem of universal cycles for k-permutations is discussed and one new enumerating method is proposed in this paper. Accurate enumerating formulae are provided when . 相似文献
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THE NUMBER OF ROOTED NEARLY CUBIC C-NETS 总被引:2,自引:0,他引:2
1. IntroductionW.T. Tutte's original papers[1--3) on the enumerative theory of rooted planar maps havebrought forth a series of papers on enumerating triangulations. The enumeration of generalrooted planar maps has then also been investigated and a number of elegant results havebeen obtained, although relatively fewer than that of triangulations. As the dual case oftriangulations, the enumerative theory of cubic maps has also been developed, though thereare a lot of problems waiting for solut… 相似文献
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JunLiangCAI YahPeiLIU 《数学学报(英文版)》2005,21(1):215-224
This paper provides some functional equations satisfied by the generating functions for enumerating general rooted planar maps with up to three parameters. Furthermore, the generating functions can be obtained explicitly by employing the Lagrangian inversion. This is also an answer to an open problem in 1989. 相似文献
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ENUMERATING ROOTED EULERIAN PLANAR MAPS 总被引:2,自引:0,他引:2
1 IntroductionSince Thtte's papers oll enunlerating planar InaPs in [7,8] published iu the beginlling Ofsixties, the enumerative theory has been developed greatly up to now. The enumeration ofgenera1 Eulerian planar maps is dependent on two paranleters as the valency of rooted vertexalld the uunther of edges Of the nmps. Y.P.Liu found tl1e functional equation firstly for thenlaPs aud then obtained the number of general rooted Elllerian planar maPs with the nuntherof edges given in 1989[1].… 相似文献
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This paper provides the parametric expressions satisfied by the enumerating functions for rooted nearly cubicc-nets with the size and/or the root-vertex valency of the maps as the parameters via nonseparable nearly cubic maps. On this
basis, two explicit expressions of the functions can be derived by employing Lagrangian inversion.
This Research is supported by National Natural Science Foundation of China (No. 19831080). 相似文献
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It is well known that singular maps (i. e. ,those have only one face on a surface)play a key role in the theory of up-embeddability of graphs. In this paper the number of rooted singular maps on the Klein bottle is studied. An explicit form of the enumerating function according to the root-valency and the size of the map is determined. Further ,an expression of the vertex partition function is also found. 相似文献
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In this article, the authors discuss two kinds of new planar maps: pan-fan maps and circuit boundary maps, and provide explicit expressions about their enumerating functions with different parameters. Meanwhile, two explicit counting formulas for circuit cubic boundary maps with two parameters; the size and the valency of the root-face, are also extracted. 相似文献