Immersed disks, slicing numbers and concordance unknotting numbers
نویسندگان
چکیده
منابع مشابه
Unknotting Numbers of Alternating Knot and Link Families
After proving a theorem about the general formulae for the signature of alternating knot and link families, we distinguished all families of knots obtained from generating alternating knots with at most 10 crossings and alternating links with at most 9 crossings, for which the unknotting (unlinking) number can be confirmed by using the general formulae for signatures.
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We show how the signed evaluations of link polynomials can be used to calculate unknotting numbers. We use the Lickorish-Millett value of the Jones polynomial to show that any achiral knot with determinant divisible by 3 does not have unknotting number one, and Jones’ value of the Brandt-Lickorish-Millett-Ho polynomial Q to calculate the unknotting numbers of 816, 949 and 6 further new entries ...
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The Zarankiewicz number z(b; s) is the maximum size of a subgraph of Kb,b which does not contain Ks,s as a subgraph. The two-color bipartite Ramsey number b(s, t) is the smallest integer b such that any coloring of the edges of Kb,b with two colors contains a Ks,s in the rst color or a Kt,t in the second color.In this work, we design and exploit a computational method for bounding and computing...
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What is the maximum number of edges of the d-dimensional hypercube, denoted by S d k , that can be sliced by k hyperplanes? This question on combinatorial properties of Euclidean geometry arising from linear separability considerations in the theory of Perceptrons has become an issue on its own. We use computational and combinatorial methods to obtain new bounds for S d k , d 8. These strengthe...
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A family of disks is said to have the property T (k) if any k members of the family have a common line transversal. We call a family of unit diameter disks t-disjoint if the distances between the centers are greater than t. We consider for each natural number k ≥ 3, the infimum tk of the distances t for which any finite family of t-disjoint unit diameter disks with the property T (k) has a line...
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ژورنال
عنوان ژورنال: Communications in Analysis and Geometry
سال: 2016
ISSN: 1019-8385,1944-9992
DOI: 10.4310/cag.2016.v24.n5.a8