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ENUMERATION OF CHORD DIAGRAMS AND AN UPPER BOUND FOR VASSILIEV INVARIANTS
We treat an enumeration problem of chord diagrams, which is shown to yield an upper bound for the dimension of the space of Vassiliev invariants for knots. We give an asymptotical estimate for thisExpand
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Polynomial values, the linking form and unknotting numbers
We show how the signed evaluations of link polynomials can be used to calculate unknotting numbers. We use the Jones-Rong value of the Brandt-Lickorish-Millett-Ho polynomial Q to calculate theExpand
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PROPERTIES OF CLOSED 3-BRAIDS
We classify the positive braid words with Morton-Williams-Franks bound 3 and show that closed positive braids of braid index 3 are closed positive 3-braids. Then we show that 3-braid links with givenExpand
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On the number of chord diagrams
  • A. Stoimenow
  • Mathematics, Computer Science
  • Discret. Math.
  • 6 May 2000
TLDR
We show that chord diagrams are basic objects in the theory of Vassiliev invariants for knots. Expand
  • 21
  • 3
On polynomials and surfaces of variously positive links
It is known that the minimal degree of the Jones polynomial of a positive knot is equal to its genus, and the minimal coefficient is $1$, with a similar relation for links. We extend this result toExpand
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Problems on invariants of knots and 3-manifolds
This is a list of open problems on invariants of knots and 3-manifolds with expositions of their history, background, significance, or importance. This list was made by editing open problems given inExpand
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On the crossing number of positive knots and braids and braid index criteria of Jones and Morton-Williams-Franks
We give examples of knots with some unusual properties of the crossing number of positive diagrams or strand number of positive braid representations. In particular we show that positive braid knotsExpand
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  • 2
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Coefficients and non-triviality of the Jones polynomial
Abstract Using an involved study of the Kauffman bracket, we give formulas for the second and third coefficient of the Jones polynomial in semiadequate diagrams. As applications, we show that severalExpand
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  • 2
On the unknotting number of minimal diagrams
  • A. Stoimenow
  • Computer Science, Mathematics
  • Math. Comput.
  • 1 October 2003
TLDR
We give examples of knots where the difference between minimal and maximal unknotting number of minimal crossing number diagrams grows beyond any extent. Expand
  • 6
  • 2
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Positive knots, closed braids and the Jones polynomial
Using the recent Gaus diagram formulas for Vassiliev invariants of Polyak-Viro-Fiedler and combining these formulas with the Bennequin inequality, we prove several inequalities for positive knotsExpand
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