Computations of quandle 2-cocycle knot invariants without explicit 2-cocycles [0.03%]
无需明确2-余胞腔的链环2-余胞腔不变量的计算方法
W Edwin Clark,Larry A Dunning,Masahico Saito
W Edwin Clark
We explore a knot invariant derived from colorings of corresponding 1-tangles with arbitrary connected quandles. When the quandle is an abelian extension of a certain type the invariant is equivalent to the quandle 2-cocycle invariant. We c...
Algebraic properties of quandle extensions and values of cocycle knot invariants [0.03%]
拟群扩张的代数性质及陪集结不变量的值分布问题
W Edwin Clark,Masahico Saito
W Edwin Clark
Quandle 2-cocycles define invariants of classical and virtual knots, and extensions of quandles. We show that the quandle 2-cocycle invariant with respect to a non-trivial 2-cocycle is constant, or takes some other restricted form, for clas...
Quandle coloring and cocycle invariants of composite knots and abelian extensions [0.03%]
复合结和阿贝尔扩张的拟群染色及余循环不变量
W Edwin Clark,Masahico Saito,Leandro Vendramin
W Edwin Clark
Quandle colorings and cocycle invariants are studied for composite knots, and applied to chirality and abelian extensions. The square and granny knots, for example, can be distinguished by quandle colorings, so that a trefoil and its mirror...
W Edwin Clark,Mohamed Elhamdadi,Masahico Saito et al.
W Edwin Clark et al.
We present a set of 26 finite quandles that distinguish (up to reversal and mirror image) by number of colorings, all of the 2977 prime oriented knots with up to 12 crossings. We also show that 1058 of these knots can be distinguished from ...
Jonathan Burns,Nataša Jonoska,Masahico Saito
Jonathan Burns
A chord diagram consists of a circle, called the backbone, with line segments, called chords, whose endpoints are attached to distinct points on the circle. The genus of a chord diagram is the genus of the orientable surface obtained by thi...