MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Given any set of tiles (jordan curves) that can tile the plane, how to prove that the number of possible tilings using tiles from this set is either in bijection with the real numbers or a (possibly infinite) subset of the integers?

Two tilings are equal if they can be made to coincide by translations or rotations.

share|cite|improve this question
Crossposted from Math.SE: – Theo Buehler Oct 10 '11 at 0:53
Closed sets in complete separable metric spaces are either countable or of cardinality continuum. Once we fix the position of the first tile, the set of possible positions of each other tile is closed by the usual compactness argument (assuming your tiles are reasonable, e.g., closed sets with boundaries of zero area, etc.). – fedja Oct 10 '11 at 1:03

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.