Add to ORKGWe consider the number of colors for the colorings of links by the symmetric group $S_3$ of degree $3$. For knots, such a coloring corresponds to a Fox 3-coloring, and thus the number of colors must be 1 or 3. However, for links, there are colorings by $S_3$ with 4 or 5 colors. In this paper, we show that if a 2-bridge link admits a coloring by $S_3$ with 5 colors, then the link also admits such a coloring with only 4 colors.Comment: 11 pages, 16 figure
summary:We provide the list of all paths with at most $16$ arcs with the property that if a graph $G...
Tied links in S^3 were introduced by Aicardi and Juyumaya as standard links in S^3 equipped with som...
Knots and links can be categorized by invariants such as colorability. A knot is a three-dimensional...
Starting from the work by Jones on representations of Thompson's group $F$, subgroups of $F$ with in...
As ropes and other one dimensional extended objects, knots and links can be found in everyday life. ...
AbstractThe well-known technique of n-coloring a diagram of an oriented link l is generalized using ...
In this paper, we present necessary and sufficient combinatorial conditions for a link to be project...
A major question in Knot Theory concerns the process of trying to determine when two knots are diffe...
The notion of an (n,r)-coloring for a link diagram generalizes the idea of an n-coloring introduced ...
Obtaining HOMFLY-PT polynomials H-R1,H-...,H-Rl for arbitrary links with l components colored by arb...
We apply the twisting technique that was first introduced in \cite{CK} and later generalized in \cit...
AbstractMorton and Franks–Williams independently gave a lower bound for the braid index b(L) of a li...
We introduce a framework to analyze knots and links in an unmarked solid torus. We discuss invariant...
We generalize the Five-Color Theorem by showing that it extends to graphs with two crossings. Furthe...
We define a triply-graded invariant of links in a genus g handlebody, generalizing the colored HOMFL...
summary:We provide the list of all paths with at most $16$ arcs with the property that if a graph $G...
Tied links in S^3 were introduced by Aicardi and Juyumaya as standard links in S^3 equipped with som...
Knots and links can be categorized by invariants such as colorability. A knot is a three-dimensional...
Starting from the work by Jones on representations of Thompson's group $F$, subgroups of $F$ with in...
As ropes and other one dimensional extended objects, knots and links can be found in everyday life. ...
AbstractThe well-known technique of n-coloring a diagram of an oriented link l is generalized using ...
In this paper, we present necessary and sufficient combinatorial conditions for a link to be project...
A major question in Knot Theory concerns the process of trying to determine when two knots are diffe...
The notion of an (n,r)-coloring for a link diagram generalizes the idea of an n-coloring introduced ...
Obtaining HOMFLY-PT polynomials H-R1,H-...,H-Rl for arbitrary links with l components colored by arb...
We apply the twisting technique that was first introduced in \cite{CK} and later generalized in \cit...
AbstractMorton and Franks–Williams independently gave a lower bound for the braid index b(L) of a li...
We introduce a framework to analyze knots and links in an unmarked solid torus. We discuss invariant...
We generalize the Five-Color Theorem by showing that it extends to graphs with two crossings. Furthe...
We define a triply-graded invariant of links in a genus g handlebody, generalizing the colored HOMFL...
summary:We provide the list of all paths with at most $16$ arcs with the property that if a graph $G...
Tied links in S^3 were introduced by Aicardi and Juyumaya as standard links in S^3 equipped with som...
Knots and links can be categorized by invariants such as colorability. A knot is a three-dimensional...