24 citations · 77 across the 18 of their papers we have counts for
20 papers
Quandles with orbit series conditions
Marco Bonatto, Alissa S. Crans, Timur Nasybullov +1
We introduce the notion of an orbit series in a quandle. Using this notion we define four families of quandles based on finiteness conditions on their orbit series. Intuitively, th…
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…
Graphs admitting only constant splines
Katie Anders, Alissa Crans, Briana Foster-Greenwood +2
We study {\em generalized graph splines,} introduced by Gilbert, Viel, and the last author. For a large class of rings, we characterize the graphs that only admit constant splines.…
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.
Crossed modules of racks
Alissa S. Crans, Friedrich Wagemann
We generalize the notion of a crossed module of groups to that of a crossed module of racks. We investigate the relation to categorified racks, namely strict 2-racks, and trunk-lik…