Geodesic
On an alternative stratification of knots
Teoretičeskaâ i matematičeskaâ fizika, Tome 216 (2023) no. 1, pp. 20-35

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

We introduce anЁalternative stratification of knots: by the size of the lattice on which a knot can be first met. Using this classification, we find the fraction of unknots and knots with more than $10$ minimal crossings inside different lattices and answer the question of which knots can be realized inside $3\times 3$ and $5\times 5$ lattices. In accordance with previous research, the fraction of unknots decreases exponentially with the growth of the lattice size. Our computational results are consistent with theoretical estimates for the number of knots with a fixed crossing number inside lattices of a given size.
Keywords: knot theory, knots classification, lattice knot.
Mots-clés : Jones polynomial 
@article{TMF_2023_216_1_a1,
     author = {E. N. Lanina and A. V. Popolitov and N. S. Tselousov},
     title = {On an alternative stratification of knots},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {20--35},
     publisher = {mathdoc},
     volume = {216},
     number = {1},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2023_216_1_a1/}
}
TY  - JOUR
AU  - E. N. Lanina
AU  - A. V. Popolitov
AU  - N. S. Tselousov
TI  - On an alternative stratification of knots
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2023
SP  - 20
EP  - 35
VL  - 216
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_2023_216_1_a1/
LA  - ru
ID  - TMF_2023_216_1_a1
ER  - 
%0 Journal Article
%A E. N. Lanina
%A A. V. Popolitov
%A N. S. Tselousov
%T On an alternative stratification of knots
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2023
%P 20-35
%V 216
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_2023_216_1_a1/
%G ru
%F TMF_2023_216_1_a1
E. N. Lanina; A. V. Popolitov; N. S. Tselousov. On an alternative stratification of knots. Teoretičeskaâ i matematičeskaâ fizika, Tome 216 (2023) no. 1, pp. 20-35. http://geodesic.mathdoc.fr/item/TMF_2023_216_1_a1/