158,386 research outputs found
A few weight systems arising from intersection graphs
We show that the adjacency matrices of the intersection graphs of chord
diagrams satisfy the 2-term relations of Bar-Natan and Garoufalides [bg], 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 {\it 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.Comment: 20 pages. This version has been substantially revised. The results
are largely the same, but the proofs have been reconceptualized in terms of
various 2-term relations on chord diagrams and graph
Semidefinite descriptions of the convex hull of rotation matrices
We study the convex hull of , thought of as the set of
orthogonal matrices with unit determinant, from the point of view of
semidefinite programming. We show that the convex hull of is doubly
spectrahedral, i.e. both it and its polar have a description as the
intersection of a cone of positive semidefinite matrices with an affine
subspace. Our spectrahedral representations are explicit, and are of minimum
size, in the sense that there are no smaller spectrahedral representations of
these convex bodies.Comment: 29 pages, 1 figur
A note on generalizations of strict diagonal dominance for real matrices
AbstractWe investigate classes of real square matrices possessing some weakened from of strict diagonal dominance of a real matrix whose diagonal entries are all positive. The intersection of each one of these classes with the set of all real matrices, with nonpositive off-diagonal elements, coincides with the set of all nonsingular M- matrices
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