On Diagram Formulas for Knot Invariants
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Geometric topology, discrete geometry, and set theory, Tome 252 (2006), pp. 10-17.

Voir la notice de l'article provenant de la source Math-Net.Ru

Several years ago, combinatorial-diagram formulas for two basis Vassiliev invariants of the fourth order were announced. In this paper, it is shown that these formulas do not determine knot invariants.
@article{TM_2006_252_a1,
     author = {S. V. Alenov and V. P. Leksin},
     title = {On {Diagram} {Formulas} for {Knot} {Invariants}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {10--17},
     publisher = {mathdoc},
     volume = {252},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2006_252_a1/}
}
TY  - JOUR
AU  - S. V. Alenov
AU  - V. P. Leksin
TI  - On Diagram Formulas for Knot Invariants
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2006
SP  - 10
EP  - 17
VL  - 252
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TM_2006_252_a1/
LA  - ru
ID  - TM_2006_252_a1
ER  - 
%0 Journal Article
%A S. V. Alenov
%A V. P. Leksin
%T On Diagram Formulas for Knot Invariants
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2006
%P 10-17
%V 252
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TM_2006_252_a1/
%G ru
%F TM_2006_252_a1
S. V. Alenov; V. P. Leksin. On Diagram Formulas for Knot Invariants. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Geometric topology, discrete geometry, and set theory, Tome 252 (2006), pp. 10-17. http://geodesic.mathdoc.fr/item/TM_2006_252_a1/

[1] Bar-Natan D., “On the Vassiliev knot invariants”, Topology, 34 (1995), 423–472 | DOI | MR | Zbl

[2] Vasilev V.A., Topologiya dopolnenii k diskriminantam, Fazis, M., 1997 | MR

[3] Kontsevich M., “Vassiliev's knot invariants”, Adv. Sov. Math., 16 (1993), 137–150 | MR | Zbl

[4] Lannes J., “Sur les invariants de Vassiliev de degreé inferieur ou égal à 3”, Enseign. Math., 39 (1993), 295–316 | MR | Zbl

[5] Östlund O.-P., A combinatorial approach to Vassiliev knot invariants, Preprint, Uppsala Univ., 1997

[6] Polyak M., Viro O., “Gauss diagram formulas for Vassiliev invariants”, Intern. Math. Res. Not., 11 (1994), 445–453 | DOI | MR | Zbl

[7] Reidemeister K., Knot theory, Chelsea Publ. Co., New York, 1948

[8] Tyurina S.D., “Diagrammnye formuly tipa Viro–Polyaka dlya invariantov konechnogo poryadka”, UMN, 54:3 (1999), 187–188 | MR

[9] Vassiliev V.A., “Combinatorial formulas for sohomology of knot spases”, Moscow Math. J., 1:1 (2001), 91–123 | MR | Zbl

[10] Allënov S.V., “Diagrammno-strelochnye formuly invariantov uzlov chetvertogo poryadka”, Fund. i prikl. matematika, 11:5 (2005), 3–17 | MR