We present an algorithm for sampling tightly confined random equilateral closed polygons in
three-space which has runtime linear in the number of edges. Using symplectic geometry …

Knots with exactly 10 sticks Page 1 April 13, 2020 16:27 WSPC/S0218-2165 134-JKTR
2050011 Journal of Knot Theory and Its Ramifications Vol. 29, No. 3 (2020) 2050011 (9 pages) …

This paper gives new upper bounds on the stick numbers of the knots 9 1 8, 1 0 1 8, 1 0 5 8,
1 0 6 6, 1 0 6 8, 1 0 8 0, 1 0 8 2, 1 0 8 4, 1 0 9 3, 1 0 1 0 0, and 1 0 1 5 2, as well as on the …

The knots 8 1, 8 2, 8 3, 8 5, 8 6, 8 7, 8 8, 8 1 0, 8 1 1, 8 1 2, 8 1 3, 8 1 4, 8 1 5, 9 7, 9 1 6, 9 2
0, 9 2 6, 9 2 8, 9 3 2, and 9 3 3 all have superbridge index equal to 4. This follows from new …

Over its history, knot theory has yielded many questions and conjectures that drove the
development not only of this field of study, but also of several other fields of mathematics …

Consider two parallel lines ℓ 1 and ℓ 2 in ℝ 3. A rail arc is an embedding of an arc in ℝ 3
such that one endpoint is on ℓ 1, the other is on ℓ 2, and its interior is disjoint from ℓ 1∪ ℓ 2 …

Previous work [C. Shonkwiler, New computations of the superbridge index, J. Knot Theory
Ramifications 29 (14)(2020) 2050096] used polygonal realizations of knots to reduce the …