Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. 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

Please read question of distinct permutation matrices with rotation at first, then new counting questions are below:

  1. For a distinct $N\times N$ zero-symmetry permutation matrix, we could rotate it 3 times and imprint all 4 images into a single canvas. Then there would be at most $4\times N$ cells selected in the final imprinted matrix. I called such matrix is Dispersed. How many Dispersed matrices for $N\times N$ permutation matrices?

  2. In the set of above imprinted matrices, some are same. Then how many distinct imprinted matrices?

Some examples of imprinted images for $4\times 4$ matrices (Please only look at row 2,3,5 and 6 which are zero-symmetry matrices. The images in left side are original, and in right side are imprinted ones. In special, images in row 5 and 6 are Dispersed):

enter image description here

share|cite|improve this question
Is this question really so hard? – gnozil Jun 26 '12 at 7:38

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.