1 citations · 3 across the 9 of their papers we have counts for
9 papers
Quandles with one non-trivial column
Nicholas Cazet
The axioms of a quandle imply that the columns of its Cayley table are permutations. This paper studies quandles with exactly one non-trivially permuted column. Their automorphism…
Symmetric quandle colorings and ribbon concordance
Nicholas Cazet
A quandle can always trivially color an orientable surface-link. This note shows that the surface-link of Yoshikawa's table cannot be colored by a symmetric dihedral…
Bounds in simple hexagonal lattice and classification of 11-stick knots
Yueheng Bao, Ari Benveniste, Marion Campisi +4
The stick number and the edge length of a knot type in the simple hexagonal lattice (sh-lattice) are the minimal numbers of sticks and edges required, respectively, to construct a…
The shadow quandle cocycle invariant of knotoids
Nicholas Cazet
This paper studies the chirality of knotoids using shadow quandle colorings and the shadow quandle cocycle invariant. The shadow coloring number and the shadow quandle cocycle inva…
The stick number of rail arcs
Nicholas Cazet
Consider two parallel lines and in . A rail arc is an embedding of an arc in such that one endpoint is on , the other is on $…
On the triple point number of surface-links in Yoshikawa's table
Nicholas Cazet
Yoshikawa made a table of knotted surfaces in R^4 with ch-index 10 or less. This remarkable table is the first to enumerate knotted surfaces analogous to the classical prime knot t…
Surface-link families with arbitrarily large triple point number
Nicholas Cazet
Analogous to a classical knot diagram, a surface-link can be generically projected to 3-space and given crossing information to create a broken sheet diagram. The triple point numb…
Vertex distortion detects the unknot
Marion Campisi, Nicholas Cazet, David Crncevic +5
The first two authors introduced vertex distortion and showed that the vertex distortion of the unknot is trivial. It was conjectured that the vertex distortion of a knot is trivia…
Vertex distortion of lattice knots
Marion Campisi, Nicholas Cazet
The vertex distortion of a lattice knot is the supremum of the ratio of the distance between a pair of vertices along the knot and their distance in the l1-norm. We show analogous…