# [R] Permutations

Peter Dalgaard BSA p.dalgaard at biostat.ku.dk
Tue Sep 26 10:42:38 CEST 2000

Torsten Hothorn <Torsten.Hothorn at rzmail.uni-erlangen.de> writes:

> Hi,
>
> this is maybe not a real R problem but I want to solve this in R ;-)
>
> Consider the set of all permutations of 1:N (=: S, say) and a fixed
> element a from S. I now need to compute the number of permutations s from
> S which are elementwise less or equal to a: | { s \in S | s <= a } |
>
> Of cource, backtracking using a tree structure is possible. Does anyone
> know an efficient way?

Er, "elementwise less than or equal"? Maybe I got off on the wrong
foot today, but if you mean what I think you mean, I get

N can only be where it is in  a  or it would replace something smaller
N-1 could be where it is or where N was, but N mustn't move
...

I.e. I'd get the answer to be 1, namely a itself.

--
O__  ---- Peter Dalgaard             Blegdamsvej 3
c/ /'_ --- Dept. of Biostatistics     2200 Cph. N
(*) \(*) -- University of Copenhagen   Denmark      Ph: (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)             FAX: (+45) 35327907
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