Questions tagged [topology]
For challenges related to topology the mathematical study of open sets.
21 questions
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Decide Equality of Closed Surfaces
Objective
Given two closed surfaces (a.k.a. closed 2-manifolds), decide whether they're homeomorphic.
Introduction
In lay terms, a closed surface is a finite-sized shape that resembles a flat plane ...
16
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15
answers
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Find separating sets
Two points pand q in a topological space can be separated if there are open sets U and ...
5
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1
answer
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Triangularly embed a graph on a surface
This challenge arises from a claim made in a MathOverflow answer and a paper linked in that answer which seems to back up the claim:
Searching for triangular embeddings is much quicker than ...
12
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2
answers
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Classify a surface from its fundamental polygon
This question is an extension of Who's that Polygon? to arbitrary numbers of sides.
A fundamental polygon for a surface is an polygon with a prescribed pairing for all its \2ドルn\$ sides, each ...
14
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7
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Euler characteristic of a binary matrix
A binary matrix represents a shape in the plane. 1 means a unit square at that position. 0 means nothing. The background is <...
47
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0
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Topologically distinct ways of dissecting a square into rectangles
I was asked by OEIS contributor Andrew Howroyd to post a Code Golf Challenge to extend OEIS sequence A049021.
Would be super great to get a couple more terms for [...] A049021. Kind of thing [...] ...
10
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3
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Count The Genus
Objective
Given a matrix of connected box drawing characters, count its genus, the number of plane sections it encloses.
Valid input
The box drawing characters are ...
18
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9
answers
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The Koszul Sign Rule
A Bit of Background
The exterior algebra is a central object in topology and physics (for the physics concept cf. fermion). The basic rule dictating the behavior of the exterior algebra is that \$yx =...
17
votes
1
answer
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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 ...
4
votes
1
answer
307
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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 ...
17
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11
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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. ...
21
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9
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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-...
15
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16
answers
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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 ...
24
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1
answer
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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, ...
26
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9
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Verify Topology
Challenge
Given a set T of subsets of a finite set S={1,2,3,...,n}, determine whether T is a ...