6 papers · 1 filter
Danceability, A New Definition of Bridge Index
Sol Addison, Sarah Blackwell, Puttipong Pongtanapaisan +3
There are many commonly known definitions of the bridge index coming from combinatorial knot theory, Morse theory, geometry, and algebra. In this paper, we prove that the danceabil…
Searching for non-order-preserving braids algorithmically
Jonathan Johnson, Nancy Scherich, Hannah Turner
An -strand braid is order-preserving if its action on the free group preserves some bi-order of . A braid is order-preserving if and only if the link obtaine…
Congruence Subgroups of the Virtual Braid Group
Wade Bloomquist, Alexa Goldberg, Nancy Scherich
We extend the notion of congruence subgroups of the braid group to the virtual braid group using an extension of the integral Burau representation. We prove that the level 2 congru…
Computing Finite Type Invariants Efficiently
Dror Bar-Natan, Itai Bar-Natan, Iva Halacheva +1
We describe an efficient algorithm to compute finite type invariants of type by first creating, for a given knot with crossings, a look-up table for all subdiagrams of…
Danceability of twisted virtual knots
Sol Addison, Nancy Scherich, Lila Snodgrass
Over the years, several Bridges papers have delved into the concept of danceability of a knot diagram. Inspired by dancing on non-orientable surfaces, in this paper, we expand danc…
Danceability, Directed by Braid Index
Sol Addison, Nancy Scherich, Lila Snodgrass
Schaffer introduced the concept of danceability of a knot diagram. In this paper, we expand upon Schaffer's ideas to create a danceability knot invariant and show that this invaria…