24 citations · 77 across the 18 of their papers we have counts for
10 papers · 1 filter
From biquandle structures to Hom-biquandles
Eva Horvat, Alissa S. Crans
We investigate the relationship between the quandle and biquandle coloring invariant and obtain an enhancement of the quandle and biquandle coloring invariants using biquandle stru…
On the Structure of Hom Quandles
Marco Bonatto, Alissa S. Crans, Glen T. Whitney
We continue the study of the quandle of homomorphisms into a medial quandle begun in Crans and Nelson. We show that it suffices to consider only medial source quandles, and therefo…
Finite -quandles of torus and two-bridge links
Alissa S. Crans, Jim Hoste, Blake Mellor +1
We compute Cayley graphs and automorphism groups for all finite -quandles of two-bridge and torus knots and links, as well as torus links with an axis.
Hom Quandles
Alissa S. Crans, Sam Nelson
If is an abelian quandle and is a quandle, the hom set of quandle homomorphisms from to has a natural quandle structure. We exploit this fact to…
Torsion in one-term distributive homology
Alissa S. Crans, Józef H. Przytycki, Krzysztof K. Putyra
The one-term distributive homology was introduced by J.H.Przytycki as an atomic replacement of rack and quandle homology, which was first introduced and developed by R.Fenn, C.Rour…
The forbidden number of a knot
Alissa Crans, Sandy Ganzell, Blake Mellor
Every classical or virtual knot is equivalent to the unknot via a sequence of extended Reidemeister moves and the so-called forbidden moves. The minimum number of forbidden moves n…
Polynomial knot and link invariants from the virtual biquandle
Alissa S. Crans, Allison Henrich, Sam Nelson
The Alexander biquandle of a virtual knot or link is a module over a 2-variable Laurent polynomial ring which is an invariant of virtual knots and links. The elementary ideals of t…
Enhancements of the rack counting invariant via N-reduced dynamical cocycles
Alissa S. Crans, Sam Nelson, Aparna Sarkar
We introduce the notion of N-reduced dynamical cocycles and use these objects to define enhancements of the rack counting invariant for classical and virtual knots and links. We pr…
Cocycle Deformations of Algebraic Identities and R-matrices
J. Scott Carter, Alissa Crans, Mohamed Elhamdadi +1
For an arbitrary identity L=R between compositions of maps L and R on tensors of vector spaces V, a general construction of a 2-cocycle condition is given. These 2-cocycles corresp…
Cohomology of Categorical Self-Distributivity
J. Scott Carter, Alissa Crans, Mohamed Elhamdadi +1
We define self-distributive structures in the categories of coalgebras and cocommutative coalgebras. We obtain examples from vector spaces whose bases are the elements of finite qu…