共查询到20条相似文献,搜索用时 68 毫秒
1.
Emmanuel Ferrand 《Proceedings of the American Mathematical Society》2002,130(4):1169-1176
It is proved in this note that the analogues of the Bennequin inequality which provide an upper bound for the Bennequin invariant of a Legendrian knot in the standard contact three dimensional space in terms of the least degree in the framing variable of the HOMFLY and the Kauffman polynomials are not sharp. Furthermore, the relationships between these restrictions on the range of the Bennequin invariant are investigated, which leads to a new simple proof of the inequality involving the Kauffman polynomial.
2.
Tatsuya Tsukamoto 《Proceedings of the American Mathematical Society》2000,128(6):1859-1867
Recently it has been proved that if and only if two knots and have the same value for the Vassiliev invariant of type two, then can be deformed into by a finite sequence of clasp-pass moves. In this paper, we determine the difference of the values of the Vassiliev invariant of type three between two knots which can be deformed into each other by a clasp-pass move.
3.
Vassiliev invariants of type two for a link 总被引:1,自引:0,他引:1
Hitoshi Murakami 《Proceedings of the American Mathematical Society》1996,124(12):3889-3896
We show that any type two Vassiliev invariant of a link can be expressed as a linear combination of the second coefficients of the Conway polynomials of its components and a quadratic expression of linking numbers.
4.
In Bataineh (2003) [2] we studied the type one invariants for knots in the solid torus. In this research we study the type one invariants for n-component links in the solid torus by generalizing Aicardi's invariant for knots in the solid torus to n-component links in the solid torus. We show that the generalized Aicardi's invariant is the universal type one invariant, and we show that the generalized Aicardi's invariant restricted to n-component links in the solid torus with zero winding number for each component is equal to an invariant we define using the universal cover of the solid torus. We also define and study a geometric invariant for n-component links in the solid torus. We give a lower bound on this invariant using the type one invariants, which are easy to calculate, which helps in computing this geometric invariant, which is usually hard to calculate. 相似文献
5.
A. Stoimenow 《Proceedings of the American Mathematical Society》2001,129(7):2141-2156
We prove that any non-hyperbolic genus one knot except the trefoil does not have a minimal canonical Seifert surface and that there are only polynomially many in the crossing number positive knots of given genus or given unknotting number.
6.
V. L. Kurakin 《Mathematical Notes》2006,80(3-4):387-395
Suppose that R is a commutative Artinian chain ring, A is an m × m matrix over R, and S is a discrete valuation ring such that R is a homomorphic image of S. We consider m ideals in the polynomial ring over S that are similarity invariants for matrices over R, i.e., these ideals coincide for similar matrices. It is shown that the new invariants are stronger than the Fitting invariants, and that new invariants solve the similarity problem for 2 × 2 matrices over R. 相似文献
7.
We generalize Brylawski’s formula of the Tutte polynomial of a tensor product of matroids to colored connected graphs, matroids,
and disconnected graphs. Unlike the non-colored tensor product where all edges have to be replaced by the same graph, our
colored generalization of the tensor product operation allows individual edge replacement. The colored Tutte polynomials we
compute exists by the results of Bollobás and Riordan. The proof depends on finding the correct generalization of the two
components of the pointed Tutte polynomial, first studied by Brylawski and Oxley, and on careful enumeration of the connected
components in a tensor product. Our results make the calculation of certain invariants of many composite networks easier,
provided that the invariants are obtained from the colored Tutte polynomials via substitution and the composite networks are
represented as tensor products of colored graphs. In particular, our method can be used to calculate (with relative ease)
the expected number of connected components after an accident hits a composite network in which some major links are identical
subnetworks in themselves.
相似文献
8.
We study relations between the Alexander–Conway polynomial L and Milnor higher linking numbers of links from the point of view of finite-type (Vassiliev) invariants. We give a formula for the first non-vanishing coefficient of L of an m-component link L all of whose Milnor numbers μi1…ip vanish for pn. We express this coefficient as a polynomial in Milnor numbers of L. Depending on whether the parity of n is odd or even, the terms in this polynomial correspond either to spanning trees in certain graphs or to decompositions of certain 3-graphs into pairs of spanning trees. Our results complement determinantal formulas of Traldi and Levine obtained by geometric methods. 相似文献
9.
10.
Let K⊂S3, and let denote the preimage of K inside its double branched cover, Σ(S3,K). We prove, for each integer n>1, the existence of a spectral sequence whose E2 term is Khovanov's categorification of the reduced n-colored Jones polynomial of (mirror of K) and whose E∞ term is the knot Floer homology of (when n odd) and of (S3,K#Kr) (when n even). A corollary of our result is that Khovanov's categorification of the reduced n-colored Jones polynomial detects the unknot whenever n>1. 相似文献
11.
Thang T.Q. Lê 《Advances in Mathematics》2006,207(2):782-804
We study relationships between the colored Jones polynomial and the A-polynomial of a knot. The AJ conjecture (of Garoufalidis) that relates the colored Jones polynomial and the A-polynomial is established for a large class of two-bridge knots, including all twist knots. We formulate a weaker conjecture and prove that it holds for all two-bridge knots. Along the way we also calculate the Kauffman bracket skein module of the complements of two-bridge knots. Some properties of the colored Jones polynomial are established. 相似文献
12.
Roger Labahn 《Order》1992,9(4):349-355
In the n-dimensional cube, we determine the maximum size of antichains having a lower shadow of exactly m elements in the k-th level. 相似文献
13.
Carsten Thomassen 《Discrete Mathematics》2006,306(23):3145-3153
We prove that, for every fixed surface S, there exists a largest positive constant c such that every 5-colorable graph with n vertices on S has at least c·2n distinct 5-colorings. This is best possible in the sense that, for each sufficiently large natural number n, there is a graph with n vertices on S that has precisely c·2n distinct 5-colorings. For the sphere the constant c is , and for each other surface, it is a finite problem to determine c. There is an analogous result for k-colorings for each natural number k>5. 相似文献
14.
Bhalchandra D. Thatte 《Journal of Graph Theory》2020,93(2):181-202
Previously we showed that many invariants of a graph can be computed from its abstract induced subgraph poset, which is the isomorphism class of the induced subgraph poset, suitably weighted by subgraph counting numbers. In this paper, we study the abstract bond lattice of a graph, which is the isomorphism class of the lattice of distinct unlabelled connected partitions of a graph, suitably weighted by subgraph counting numbers. We show that these two abstract posets can be constructed from each other except in a few trivial cases. The constructions rely on certain generalisations of a lemma of Kocay in graph reconstruction theory to abstract induced subgraph posets. As a corollary, trees are reconstructible from their abstract bond lattice. We show that the chromatic symmetric function and the symmetric Tutte polynomial of a graph can be computed from its abstract induced subgraph poset. Stanley has asked if every tree is determined up to isomorphism by its chromatic symmetric function. We prove a counting lemma, and indicate future directions for a study of Stanley's question. 相似文献
15.
Taizo Kanenobu & Yasuyuki Miyazawa 《数学研究通讯:英文版》2009,25(5):433-460
An $H(2)$-move is a local move of a knot which is performed by adding a
half-twisted band. It is known an $H(2)$-move is an unknotting operation. We define
the $H(2)$-unknotting number of a knot $K$ to be the minimum number of $H(2)$-moves
needed to transform K into a trivial knot. We give several methods to estimate the $H(2)$-unknotting number of a knot. Then we give tables of $H(2)$-unknotting numbers
of knots with up to 9 crossings. 相似文献
16.
F. Jaeger has shown that up to a ± sign the evaluation at (j, j
2) of the Tutte polynomial of a ternary matroid can be expressed in terms of the dimension of the bicycle space of a representation over GF(3). We give a short algebraic proof of this result, which moreover yields the exact value of ±, a problem left open in Jaeger's paper. It follows that the computation of t(j, j
2) is of polynomial complexity for a ternary matroid.E. Gioan: C.N.R.S., MontpellierM. Las Vergnas: C.N.R.S., Paris 相似文献
17.
18.
In this article we deal with a Hamiltonial of the form H(v) = Ho + A(v) where Ho is a self-adjoint bounded or unbounded operator on a Hilbert space and A(v) is a bounded self-adjoint perturbation depending on a real parameter v. In quantum mechanics a variety of results has been obtained by taking formally the derivative of the eigenvectors and eigenvalues of H(v).The differentiability of the eigenvectors and eigenvalues has been rigorously proved under several assumptions. Among these assumptions is the assumption that the eigenvalues are simple and the assumption that the perturbation A(v) is a uniformly bounded self-adjoint operator. A part of this article is dealing with examples, which show that these two assumptions are essential. The rest of this article is devoted to different applications concerning asymptotic relations of eigenvalues and a result for the solutions of the equation dy/dt= M(t)y in an abstract infinite dimensional Hilbert space, where iM(t)(12=-1) is self-adjoint for every t in an interval. This result finds a succesful application to the theory of Toda and Langmuir lattices. 相似文献
19.
20.
A Note on the Nonparametric
Least-squares Test for Checking a Polynomial Relationship 总被引:1,自引:0,他引:1
Chang-linMei Shu-yuanHe Yan-huaWang 《应用数学学报(英文版)》2003,19(3):511-520
Recently, Gijbels and Rousson[6] suggested a new approach, called nonparametric least-squares test, to check polynomial regression relationships. Although this test procedure is not only simple but also powerful in most cases, there are several other parameters to be chosen in addition to the kernel and bandwidth.As shown in their paper, choice of these parameters is crucial but sometimes intractable. We propose in this paper a new statistic which is based on sample variance of the locally estimated pth derivative of the regression function at each design point. The resulting test is still simple but includes no extra parameters to be determined besides the kernel and bandwidth that are necessary for nonparametric smoothing techniques. Comparison by simulations demonstrates that our test performs as well as or even better than Gijbels and Rousson‘s approach.Furthermore, a real-life data set is analyzed by our method and the results obtained are satisfactory. 相似文献