Pseudodiagrams are knot or link diagrams where some of the crossing information is missing. Pseudoknots are equivalence classes of pseudodiagrams, where equivalence is generated by a natural set of Reidemeister moves. In this paper, we introduce a Gauss-diagrammatic theory for pseudoknots which gives rise to the notion…
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11 results for “pseudoknots”
Pseudodiagrams are diagrams of knots where some information about which strand goes over/under at certain crossings may be missing. Pseudoknots are equivalence classes of pseudodiagrams, with equivalence defined by a class of Reidemeister-type moves. In this paper, we introduce two natural extensions of classical knot …
Psybrackets define invariants for complex knots and links.
problem Defining invariants for complex knots and links.
method Introduced algebraic structures called psybrackets and used them to define invariants of pseudoknots and singular knots and links.
result Examples and computations provided for the invariants defined.
When the signed weighted resolution set was defined as an invariant of pseudoknots, it was unknown whether this invariant was complete. Using the Gauss-diagrammatic invariants of pseudoknots introduced by Dorais et al, we show that the signed were-set cannot distinguish all non-equivalent pseudoknots. This goal is achi…
Psyquandle Coloring Quiversmath.GT
Enhances psyquandle invariants for singular and pseudoknots.
problem Counting invariants for singular knots and pseudoknots.
method Uses quivers to extend in-degree polynomial invariants.
result Obtains biquandle coloring quivers and in-degree polynomial invariants.
The Theory of Pseudoknotsmath.GT
Classical knots in can be represented by diagrams in the plane. These diagrams are formed by curves with a finite number of transverse crossings, where each crossing is decorated to indicate which strand of the knot passes over at that point. A pseudodiagram is a knot diagram that may be missing crossing…
The notion of a pseudoknot is defined as an equivalence class of knot diagrams that may be missing some crossing information. We provide here a topological invariant schema for pseudoknots and their relatives, 4-valent rigid vertex spatial graphs and singular knots, that is obtained by replacing unknown crossings or ve…
Psyquandle Bracketsmath.GT
Extends biquandle brackets to psyquandles for knot and pseudoknot invariants.
problem Counting invariants for singular and pseudoknots.
method Define quantum enhancements of psyquandle counting invariant.
result Proper quantum enhancements for singular and pseudoknots.
Enhances psyquandle counting invariants using cocycles.
problem Improving the counting invariant of pseudoknots and singular knots.
method Defining enhancements via biquandle 2-cocycles and new functions.
result New polynomial invariants that are proper enhancements and not determined by the Jablan polynomial.
We generalize the notion of biquandles to psyquandles and use these to define invariants of oriented singular links and pseudolinks. In addition to psyquandle counting invariants, we introduce Alexander psyquandles and corresponding invariants such as Alexander psyquandle polynomials and Alexander-Gröbner psyquandle in…
E2Efold predicts RNA secondary structures better than previous methods.
problem RNA secondary structure prediction with constraints.
method End-to-end deep learning model using unrolled algorithms to enforce constraints.
result E2Efold predicts significantly better structures, especially for pseudoknotted structures.