9 citations · 38 across the 12 of their papers we have counts for
14 papers
The average genus of a 2-bridge knot is asymptotically linear
Moshe Cohen, Adam M. Lowrance
Experimental work suggests that the Seifert genus of a knot grows linearly with respect to the crossing number of the knot. In this article, we use a billiard table model for -b…
A lower bound on the average genus of a 2-bridge knot
Moshe Cohen
Experimental data from Dunfield et al using random grid diagrams suggests that the genus of a knot grows linearly with respect to the crossing number. Using billiard table diagrams…
Crossing Numbers of Random Two-Bridge Knots
Moshe Cohen, Chaim Even-Zohar, Sunder Ram Krishnan
In a previous work, the first and third authors studied a random knot model for all two-bridge knots using billiard table diagrams. Here we present a closed formula for the distrib…
Random knots using Chebyshev billiard table diagrams
Moshe Cohen, Sunder Ram Krishnan
We use the Chebyshev knot diagram model of Koseleff and Pecker in order to introduce a random knot diagram model by assigning the crossings to be positive or negative uniformly at…
The Jones polynomials of 3-bridge knots via Chebyshev knots and billiard table diagrams
Moshe Cohen
This work presents formulas for the Kauffman bracket and Jones polynomials of 3-bridge knots using the structure of Chebyshev knots and their billiard table diagrams. In particular…
A counterexample to Question 1 of "A survey on the Turaev genus of knots"
Cody Armond, Moshe Cohen
In "A survey on the Turaev genus of knots," Champanerkar and Kofman propose several open questions. The first asks whether the polynomial whose coefficients count the number of qua…