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KNOTS, SLIPKNOTS, AND EPHEMERAL KNOTS IN RANDOM WALKS AND EQUILATERAL POLYGONS

2010; World Scientific; Volume: 19; Issue: 05 Linguagem: Inglês

10.1142/s0218216510008078

1793-6527

Kenneth C. Millett,

Caveolin-1 and cellular processes

The probability that a random walk or polygon in the 3-space or in the simple cubic lattice contains a knot goes to one at the length goes to infinity. Here, we prove that this is also true for slipknots consisting of unknotted portions, called the slipknot, that contain a smaller knotted portion, called the ephemeral knot. As is the case with knots, we prove that any topological knot type occurs as the ephemeral knotted portion of a slipknot.