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This article is cited in 1 scientific paper (total in 1 paper)
Research Papers
On the growth of the number of prime knots
I. S. Alekseev, A. M. Vershik, A. V. Malyutin
St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences
Abstract:
We construct embeddings of locally free semigroups into the set of knots.
These embeddings and the results of A. Vershik, S. Nechaev, and R. Bikbov
on the logarithmic volume of locally free semigroups give a new record
lower bound on the growth rate of the number of knots with respect to the
crossing number.
Keywords:
Knot, link, braid, tangle, unicursal curve, alternating knot, prime knot,
Tait conjectures, checkerboard graph, locally free group, right-angled
Artin group, braid group, growth rate.
Received: 11.09.2023
Citation:
I. S. Alekseev, A. M. Vershik, A. V. Malyutin, “On the growth of the number of prime knots”, Algebra i Analiz, 36:1 (2024), 17–39
Linking options:
https://www.mathnet.ru/eng/aa1899 https://www.mathnet.ru/eng/aa/v36/i1/p17
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| Abstract page: | 197 | | Full-text PDF : | 5 | | References: | 42 | | First page: | 30 |
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