r - Finding all possible combinations of vector intersections?

Question

I have a set of four vectors that look like this:

[1] PRI2CO       HEISCO       PRI2CO       DIALGU       DIALGU       ALSEBL      
Levels: ALSEBL       DIALGU       HEISCO       PRI2CO  

[1] PRI2CO       TET2PA       ALSEBL       PRI2CO       ALSEBL       TET2PA      
[7] HEISCO       TET2PA      
Levels: ALSEBL       HEISCO       PRI2CO       TET2PA

I would like to generate a vector that contains all values that match between every possible combination of the four vectors. For the two above, it would contain ALESBL, HEISCO, and PRI2CO. I've been doing every combination by hand so far but its tedious and I figure there has to be a better way. I tried writing a loop for it but I'm pretty new to R and it hasn't worked yet. Here's what I've been doing:

trees.species.P234<-intersect(intersect(trees.species.P2,trees.species.P3),trees.species.P4)
> trees.species.P234
[1] "PRI2CO      " "ALSEBL      "

I was thinking a for loop that involved a factorial might do it, but I can't get it to work.

Answer 1

Here you go, using the same vectors as proposed by gadzooks:

v1 <- c("PRI2CO","HEISCO","PRI2CO","DIALGU","DIALGU","ALSEBL")
v2 <- c("PRI2CO", "TET2PA","ALSEBL","PRI2CO","ALSEBL","TET2PA","HEISCO","TET2PA")
v3 <- c("PRI2CO","HEISCO","PRI2CO","DIALGU","DIALGU","ALSEBL")
v4 <- c("PRI2CO", "TET2PA","ALSEBL","PRI2CO","ALSEBL","TET2PA","HEISCO","TET2PA")

veclist <- list(v1,v2,v3,v4)
combos <- Reduce(c,lapply(2:length(veclist), 
            function(x) combn(1:length(veclist),x,simplify=FALSE) ))

lapply(combos, function(x) Reduce(intersect,veclist[x]) )

#[[1]]
#[1] "PRI2CO" "HEISCO" "ALSEBL"
# 
#[[2]]
#[1] "PRI2CO" "HEISCO" "DIALGU" "ALSEBL"
#
#[[3]]
#[1] "PRI2CO" "HEISCO" "ALSEBL"
#etc etc