Category: Mathematics

Burnside’s Lemma: Proof and Application
In the previous post, I proved the OrbitStabilizer Theorem which states that the number of elements in an orbit of a is equal to the number of left cosets of the stabilizer of a. Burnside’s Lemma Let’s us review the Lemma once again: Where A/G is the set of orbits, and A/G is the cardinality of this set. Ag is the…

Burnside’s Lemma: OrbitStabilizer Theorem
Problem: Given a 3 by 3 grid, with 5 colors. How many different ways to color the grid, given that two configurations are considered the same if they can be reached through rotations ( 0, 90, 180, 270 degrees )? This problem was given in my Number Theory course. Somehow when I searched for the solution,…