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1.
We investigate the combinatorics of a topological space that is generated by the set of edge-weighted finite trees. This space arises by multiplying the weights of edges on paths in trees and is closely connected to tree reconstruction problems involving finite state Markov processes. We show that this space is a contractible finite CW-complex whose face poset can be described via a partial order on semilabelled forests. We then describe some combinatorial properties of this poset, showing that, for example, it is pure, thin and contractible. 相似文献
2.
Cilanne E. Boulet 《The Ramanujan Journal》2006,12(3):315-320
We present a new partition identity and give a combinatorial proof of our result. This generalizes a result of Andrews in
which he considers the generating function for partitions with respect to size, number of odd parts, and number of odd parts
of the conjugate.
2000 Mathematics Subject Classification Primary—05A17; Secondary—11P81 相似文献
3.
4.
Dennis Stanton 《The Ramanujan Journal》2009,19(1):107-113
Two q-analogues of Euler’s theorem on integer partitions with odd or distinct parts are given. A q-lecture hall theorem is given.
Supported by NSF grant DMS-0503660. 相似文献
5.
We study the discrete-time evolution of a recombination transformation in population genetics. The transformation acts on a product probability space, and its evolution can be described by a Markov chain on a set of partitions that converges to the finest partition. We describe the geometric decay rate to this limit and the quasi-stationary behavior of the Markov chain when conditioned on the event that the chain does not hit the limit. 相似文献
6.
C.M. da Fonseca 《Discrete Mathematics》2009,309(8):2519-757
Given partitions R and S with the same weight, the Robinson-Schensted-Knuth correspondence establishes a bijection between the class A(R,S) of (0, 1)-matrices with row sum R and column sum S and pairs of Young tableaux of conjugate shapes λ and λ∗, with S?λ?R∗. An algorithm for constructing a matrix in A(R,S) whose insertion tableau has a prescribed shape λ, with S?λ?R∗, is provided. We generalize some recent constructions due to R. Brualdi for the extremal cases λ=S and λ=R∗. 相似文献
7.
Andrew V. Sills 《Journal of Combinatorial Theory, Series A》2008,115(1):67-83
We provide a bijective map from the partitions enumerated by the series side of the Rogers-Selberg mod 7 identities onto partitions associated with a special case of Basil Gordon's combinatorial generalization of the Rogers-Ramanujan identities. The implications of applying the same map to a special case of David Bressoud's even modulus analog of Gordon's theorem are also explored. 相似文献
8.
For any 2D triangulation τ, the 1-skeleton mesh of τ is the wireframe mesh defined by the edges of τ, while that for any 3D triangulation τ, the 1-skeleton and the 2-skeleton meshes, respectively, correspond to the wireframe mesh formed by the edges of τ and the “surface” mesh defined by the triangular faces of τ. A skeleton-regular partition of a triangle or a tetrahedra, is a partition that globally applied over each element of a conforming mesh (where the intersection of adjacent elements is a vertex or a common face, or a common edge) produce both a refined conforming mesh and refined and conforming skeleton meshes. Such a partition divides all the edges (and all the faces) of an individual element in the same number of edges (faces). We prove that sequences of meshes constructed by applying a skeleton-regular partition over each element of the preceding mesh have an associated set of difference equations which relate the number of elements, faces, edges and vertices of the nth and (n−1)th meshes. By using these constitutive difference equations we prove that asymptotically the average number of adjacencies over these meshes (number of triangles by node and number of tetrahedra by vertex) is constant when n goes to infinity. We relate these results with the non-degeneracy properties of longest-edge based partitions in 2D and include empirical results which support the conjecture that analogous results hold in 3D. 相似文献
9.
Morgen-Scot剖分上样条空间的维数依赖于剖分的几何性质,本文证明了Diener1990年提出的猜想对r=4是不正确的,需要修正. 相似文献
10.
For compact Riemann surfaces, the collar theorem and Bers’ partition theorem are major tools for working with simple closed
geodesics. The main goal of this article is to prove similar theorems for hyperbolic cone-surfaces. Hyperbolic two-dimensional
orbifolds are a particular case of such surfaces. We consider all cone angles to be strictly less than π to be able to consider
partitions.
Emily B. Dryden—partially supported by the US National Science Foundation grant DMS-0306752.
Hugo Parlier—supported by the Swiss National Science Foundation grants 21-57251.99 and 20-68181.02. 相似文献