Questions tagged [topology]

For challenges related to topology the mathematical study of open sets.

12 questions
196 views

Multiplication in the Steenrod Algebra

Here's yet another Steenrod algebra question. Summary of the algorithm: I have a procedure that replaces a list of positive integers with a list of lists of positive integers. You need to repeatedly ...
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Generate basis elements of the Steenrod algebra

The Steenrod algebra is an important algebra that comes up in algebraic topology. The Steenrod algebra is generated by operators called "Steenrod squares," one exists for each positive integer i. ...
807 views

Cycles on the torus

Challenge This challenge will have you write a program that takes in two integers n and m and outputs the number non-...
757 views

Euler-Poincaré-Characteristic of Polyhedra

Given a triangulation of the surface of a polyhedron p, calculate its Euler-Poincaré-Characteristic χ(p) = V-E+F, where ...
486 views

Determine if a Graph is Toroidal

A simple graph is toroidal if it can be drawn on the surface of a torus without any edges intersecting. Your task is to take a simple undirected graph via any reasonable method (adjacency matrix, ...
1k views

Verify Topology

Challenge Given a set T of subsets of a finite set S={1,2,3,...,n}, determine whether T is ...
745 views

Are these braids equal?

If you are not familiar with Braid-Theory I recommend that you read this first. This question assumes that you are at least familiar with the concepts at hand and assumes you are well familiar with ...
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Klein Topololyglots

Klein is a 2D language I have designed that can be embedded on 12 different topological surfaces. A Klein program can be run on different surfaces by changing the command line arguments. The ...
327 views

Who's that Polygon?

A convenient and useful way to represent topological surfaces is with a fundamental polygon. Each side on a polygon matches to another side and can be either parallel or anti-parallel. For instance ...
218 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, ...