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JOURNALS // Algebra i Analiz // Archive

Algebra i Analiz, 2024 Volume 36, Issue 1, Pages 17–39 (Mi aa1899)

This article is cited 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



© Steklov Math. Inst. of RAS, 2024