A Few Weight Systems Arising from Intersection Graphs
نویسنده
چکیده
We show that the adjacency matrices of the intersection graphs of chord diagrams satisfy the 2-term relations of Bar-Natan and Garoufalides [2], and hence give rise to weight systems. Among these weight systems are those associated with the Conway and HOMFLYPT polynomials. We extend these ideas to looking at a space of marked chord diagrams modulo an extended set of 2-term relations, define a set of generators for this space, and again derive weight systems from the adjacency matrices of the (marked) intersection graphs. Among these weight systems are those associated with the Kauffman polynomial.
منابع مشابه
2 00 0 Three Weight Systems Arising from Intersection Graphs
We describe three weight systems arising from the intersection graphs of chord diagrams (also known as circle graphs). These derive from the determinant and rank of the adjacency matrix of the graph, viewed over Z 2 , and from the rank of a " marked " adjacency matrix. We show that these weight systems are exactly those given by the Conway, HOMFLYPT and Kauffman polynomials, respectively.
متن کاملSome lower bounds for the $L$-intersection number of graphs
For a set of non-negative integers~$L$, the $L$-intersection number of a graph is the smallest number~$l$ for which there is an assignment of subsets $A_v subseteq {1,dots, l}$ to vertices $v$, such that every two vertices $u,v$ are adjacent if and only if $|A_u cap A_v|in L$. The bipartite $L$-intersection number is defined similarly when the conditions are considered only for the ver...
متن کاملIntersection Graphs for String Links
We extend the notion of intersection graphs for knots in the theory of finite type invariants to string links. We use our definition to develop weight systems for string links via the adjacency matrix of the intersection graphs, and show that these weight systems are related to the weight systems induced by the Conway and Homfly polynomials.
متن کاملTwo-weight codes, graphs and orthogonal arrays
We investigate properties of two-weight codes over finite Frobenius rings, giving constructions for the modular case. A δ-modular code [15] is characterized as having a generator matrix where each column g appears with multiplicity δ|gR×| for some δ ∈ Q. Generalizing [10] and [5], we show that the additive group of a two-weight code satisfying certain constraint equations (and in particular a m...
متن کاملMutant knots and intersection graphs
We prove that if a finite order knot invariant does not distinguish mutant knots, then the corresponding weight system depends on the intersection graph of a chord diagram rather than on the diagram itself. Conversely, if we have a weight system depending only on the intersection graphs of chord diagrams, then the composition of such a weight system with the Kontsevich invariant determines a kn...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2002