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

I would like to generate fixed size sequences contained a fixed number of repeated symbols. For example how to generate sequences of size N containing exactly p symbols of one type q symbols of another, etc... where p, q, etc. < N.

In my case I want to generate sequences of size 13 containing 3 symbols denoted x, 2 symbols denoted y and 2 symbols denoted z. Blank spaces are marked with '-'

So it would look like xxxyyzz------, x-xx--y-y-zz- ... etc.

There are C(13, 3)*C(10,2)*C(8,2) ways of generating such sequences but I have no idea how to generate them.

Technically how do you describe this problem? Combinations with repetitions? Where can I find a description of algorithms to solve this? Does Knuth book describe this algorithms? Most of the solutions I find deal with generating permutations or combinations but none deal with repeated elements.


share|cite|improve this question
I think this might be more for math.SE Consider multinomial coefficients:… – Daniel Moskovich Jul 13 '11 at 17:15
Thanks for the pointer. It led to me to the correct technical description of this problem which is the enumeration of permutations of a multiset. Now I need to find an algorithm to generate this permutations. – user16416 Jul 13 '11 at 21:22
There is quite a literature on this. A google search on "permutations of a multiset generation" will give many hits. – Richard Stanley Jul 14 '11 at 0:29

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.