Entropic Niebrzydowski Tribrackets

We introduce the notion of entropic Niebrzydowski tribrackets or just entropic tribrackets, analogous to entropic (also known as abelian or medial ) quandles and biquandles. We show that if X is a finite entropic tribracket then for any tribracket T , the homset Hom(T, X) (and in particular, for any oriented link L, the homset Hom(T (L), X)) also has the structure of an entropic tribracket. This operation yields a product on the category of entropic tribrackets; we compute the operation table for entropic tribrackets of small cardinality and prove a few results. We conjecture that this structure can be used to distinguish links which have the same counting invariant with respect to a chosen entropic coloring tribracket X.Comment: 10 page

Psybrackets, Pseudoknots and Singular Knots

We introduce algebraic structures known as psybrackets and use them to define invariants of pseudoknots and singular knots and links. Psybrackets are Niebrzydowski tribrackets with additional structure inspired by the Reidemeister moves for pseudoknots and singular knots. Examples and computations are provided.Comment: 12 page