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suppose a partical can move on x-coordinate, which means it can move 0 to 1 or 1 to 2 or N-1 to N .etc, now it starts with 0, it can move one step every time, left or right (e.g. when it reaches 5, it can move right to 6 or left to 4). and after N times of moving, it reaches it original place 0, however, it never reaches 0 in the intermidate, what the number of the permulation?

Sayakiss
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stonestrong
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  • This really needs refining. I have absolutely no idea what you're asking. It also sounds suspiciously like a homework question. – christopher May 09 '13 at 09:11
  • I am sorry that i don't express clearly, now I have refined my question, if you have any idea about this, tell me, thanks :) – stonestrong May 09 '13 at 09:19
  • *what the number of the permulation?*. A permutation is re-ordering things. You're saying after `N` times of moving, it reaches `0`. Well this can be achieved by moving from `{0 --> 1}` then `{1 --> 0}`. I don't think you're giving us all the information here. – christopher May 09 '13 at 09:28
  • apologize for my poor English, Here `N` is a given variable, obviously it should be even, suppose `N` assumes 4, there is only one permulation (e.g. `{0 --> 1} {1 --> 2} {2 --> 1} {1 --> 0}`), and I was consulting the answer expressed by N – stonestrong May 09 '13 at 09:37
  • It looks like the question belongs to [math.se] and is off-topic here. – John Dvorak May 09 '13 at 09:38

1 Answers1

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I think the answer of your question is Catalan number.

In wiki page:

Cn is the number of Dyck words of length 2n. A Dyck word is a string consisting of n X's and n Y's such that no initial segment of the string has more Y's than X's (see also Dyck language). For example, the following are the Dyck words of length 6:

XXXYYY XYXXYY XYXYXY XXYYXY XXYXYY.

You can consider X is go right and Y is go left.

See http://en.wikipedia.org/wiki/Catalan_number

Sayakiss
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  • @stonestrong so vote me up plz? – Sayakiss May 09 '13 at 09:43
  • Hey, it's a variant question in `probability and computing`, the original problem is that the patical moves right with probabilty p, moves left with probability 1-p, except that it moves `0` to `1` with probabilty 1. prove `if p < 1/2 is positive recurrent, if p = 1/2 ,each state is null recurrent, and if p > 1/2, each state is transient` – stonestrong May 09 '13 at 09:52
  • I am glad to, but my reputation is below 15 :(. I will vote you up as soon as my reputation reaches 15. – stonestrong May 09 '13 at 09:55
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    @stonestrong I'm sorry but I have no idea of that problem... – Sayakiss May 09 '13 at 10:02