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 ...
16
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1answer
254 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 ...
35
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2answers
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 ...
9
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1answer
226 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, ...
23
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1answer
865 views

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 ...
33
votes
1answer
904 views

Gasket Weaving - draw a Sierpiński knot

Given an integer N >= 2, produce an image showing a Sierpiński knot of degree N. For example, here are knots of degree 2, 3, 4 and 5: Click on the images to view full size (the higher the degree the ...
145
votes
1answer
5k views

“KNOT” or “NOT”?

Write a program that processes an ASCII art representation of a tangled string and decides whether or not it can be untangled into a simple loop. The tangle is represented using the characters ...