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Publications Influence

ENUMERATION OF CHORD DIAGRAMS AND AN UPPER BOUND FOR VASSILIEV INVARIANTS

- A. Stoimenow
- Mathematics
- 1 February 1998

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 this… Expand

63 13

Polynomial values, the linking form and unknotting numbers

- A. Stoimenow
- Mathematics
- 5 May 2004

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 the… Expand

33 6- PDF

PROPERTIES OF CLOSED 3-BRAIDS

- A. Stoimenow
- Mathematics
- 19 June 2006

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 given… Expand

15 5- PDF

On the number of chord diagrams

- A. Stoimenow
- Mathematics, Computer Science
- Discret. Math.
- 6 May 2000

TLDR

21 3

On polynomials and surfaces of variously positive links

- A. Stoimenow
- Mathematics
- 22 February 2002

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 to… Expand

22 3- PDF

Problems on invariants of knots and 3-manifolds

- J. Andersen, N. Askitas, +57 authors Y. Yokota
- Mathematics
- 1 June 2004

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 in… Expand

101 2- PDF

On the crossing number of positive knots and braids and braid index criteria of Jones and Morton-Williams-Franks

- A. Stoimenow
- Mathematics
- 1 October 2001

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 knots… Expand

57 2- PDF

Coefficients and non-triviality of the Jones polynomial

- A. Stoimenow
- Mathematics
- 11 June 2006

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 several… Expand

30 2

On the unknotting number of minimal diagrams

- A. Stoimenow
- Computer Science, Mathematics
- Math. Comput.
- 1 October 2003

TLDR

6 2- PDF

Positive knots, closed braids and the Jones polynomial

- A. Stoimenow
- Mathematics
- 18 May 1998

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 knots… Expand

50 1- PDF

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