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math.GT2026
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…
math.GT2025
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…
math.GT2024
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…