# Questions tagged [knot-theory]

Knot-theory is a branch of topology that studies mathematical knots. This tag is for challenges regarding the manipulation of mathematical knots.

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### Compare Dowker Knotation

Dowker notation is a common way of representing mathematical knots. Dowker notation can be derived from a knot diagram in the following way (based on the description from the wikipedium): We will ...
245 views

### Can this knot be colored with 3 colors?

In this challenge you will be asked to take a knot and determine if it can be colored in a particular way. First we draw a diagram of the knot. We use the standard way of drawing knots where we put ...
1k views

### A Knotty situation

Given the Dowker notation of a knot and its crossing signs, calculate its bracket polynomial. Although there are more technical definitions, for this challenge it is enough to think of a knot as ...
225 views

### Number of prime knots with n crossings

A prime knot is: a non-trivial knot which cannot be written as the knot sum of two non-trivial knots. Explanation of a knot-sum: put the two knots adjacent, ... then draw two lines between them, ...
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### A Rather Knotty Conundrum

Write a program to draw a 2-D diagram of a knot based on the knot's structure. A knot is exactly what it sounds like: a loop of rope that's tied up. In mathematics, a knot diagram shows where a piece ...