The squares of a nxn checkerboard are to be colored with m colors.
Two colorings are said to be equivalent of one can be transformed into
the other by a rigid motion of the checkerboard in 2 dimensions
(no flips).How many colorings are there?
Can you explain how you got that answer? Additionally, the question says to consider the cases for n even and n odd.. but there is no other information. I don't think it has anything to do with the equivalence classes.
2007-10-28 13:00:26 · 1 answers · asked by Anthony M 1 in Science & Mathematics ➔ Mathematics
Problems of this nature generate interesting sequences. Check out The On-Line Encyclopedia of Integer Sequences! You will find the case with three colors and n x n grid, and also the 3 x 3 grid with n colors. I don't see the general case that you are posing.
http://www.research.att.com/~njas/sequences/?q=coloring&sort=0&fmt=0&language=english
2007-10-28 14:32:00 · answer #1 · answered by jsardi56 7 · 0⤊ 0⤋