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

I was reading a paper

On the page 38, under the topic The vertex hierarchy I have doubt. From where did the following term come?

enter image description here

enter image description here

I am getting no idea how they did it? Any hint will be appreciated. Thanks a lot for help.

share|cite|improve this question
You want to count vertices that has zeros at coordinates $< k$ and are non-zero at exactly $k$-th coordinate and anything at bigger coordinates. Hence, you have exactly $1$ possibility for $i < k$ (namely, zero), $n_i - 1$ possibilities for $i = k$ (anything but a zero) and $n_i$ possibilities for $i > k$ (no constraints). Multiplying it all will get you the aforementioned formula. – dtldarek Aug 22 '13 at 10:38
thanks a lot :) I got it. – monalisa Aug 22 '13 at 10:42

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.