Equivalence
Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.
Three moves, and what they cannot undo
A knot is a closed loop of string, and two knots are the same if one can be wiggled into the other. Reidemeister reduced all possible wiggling to three local pictures — which is what makes it possible to prove that a knot is knotted.
Colourings nobody can tell apart
Sixteen ways to colour four corners in two colours, and only six of them are genuinely different. The count can be got by pooling the sixteen — or by never forming a single class and instead averaging how many colourings each motion leaves untouched.
Named alongside it
The objects these essays reach for when they reach for this one.
Counting argumentCounting two waysCrossing numberCyclic groupDihedral groupGroup actionInvariantKnotLagrange theoremOrbitOrientationPermutation