8 citations · 11 across the 2 of their papers we have counts for
6 papers · 1 filter
A move on diagrams that generates S-equivalence of knots
Swatee Naik, Theodore Stanford
Two knots in three-space are S-equivalent if they are indistinguishable by Seifert matrices. We show that S-equivalence is generated by the doubled-delta move on knot diagrams. It…
On a Map From Pure Braids to Knots
Jacob Mostovoy, Theodore Stanford
We study a certain type of braid closure which resembles the plat closure but has certain advantages; for example, it maps pure braids to knots. The main results of this note are a…
Brunnian braids and some of their generalizations
Theodore Stanford
We use a variation on the commutator collection process to characterize those pure braids which become trivial when any one strand is deleted, or, more generally, those pure braids…
Braid commutators and delta finite-type invariants
Theodore B. Stanford
Delta finite-type invariants are defined analogously to finite-type invariants, using delta moves instead of crossing changes. We show that they are closely related to the lower ce…
On knot invariants which are not of finite type
Theodore Stanford, Rolland Trapp
We observe that most known results of the form "v is not a finite-type invariant" follow from two basic theorems. Among those invariants which are not of finite type, we discuss ex…
On the z-degree of the Kauffman polynomial of a tangle decomposition
Mark E. Kidwell, Theodore B. Stanford
We give an upper bound on the z-degree of the Kauffman polynomial of a link, using bridges of length greater than one which are separated in some tangle decomposition of a link dia…