Tag: Orbit-Stabilizer Theorem

  • Burnside’s Lemma: Proof and Application

    In the previous post, I proved the Orbit-Stabilizer 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: Orbit-Stabilizer 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, […]