R - Permutations between 2 or more vectors, with constraints -

i generate possible permutations between 2 or more vectors, but;

1. order important.
2. the first number must lesser second, , second must lesser third.
3. there cannot same number.

for instance:

a <- c(3, 5, 8) b <- c(8, 10, 12) c <- c(12, 15, 20) 

the first element a, second b , third c.
possible results be:

(3, 8, 12), (3, 8, 15), (3, 8, 20), (3, 10, 12), (3, 10, 15) , (3, 10, 20).

but there shouldn't results repeated numbers, instance:

(8, 8, 12), (8, 12, 12).

how can accomplished using r?

if understand rules correctly, should work.

a <- c(3, 5, 8) b <- c(8, 10, 12) c <- c(12, 15, 20)  f <- function(x,y) lapply(y[y>tail(x,1)], function(zz) c(x,zz)) g <- function(x,y) unlist(lapply(x,f,y=y), recursive=false)  do.call(rbind,g(g(a,b),c)) #       [,1] [,2] [,3] #  [1,]    3    8   12 #  [2,]    3    8   15 #  [3,]    3    8   20 #  [4,]    3   10   12 #  [5,]    3   10   15 #  [6,]    3   10   20 #  [7,]    3   12   15 #  [8,]    3   12   20 #  [9,]    5    8   12 # [10,]    5    8   15 # [11,]    5    8   20 # [12,]    5   10   12 # [13,]    5   10   15 # [14,]    5   10   20 # [15,]    5   12   15 # [16,]    5   12   20 # [17,]    8   10   12 # [18,]    8   10   15 # [19,]    8   10   20 # [20,]    8   12   15 # [21,]    8   12   20 

for 4 vectors, use

do.call(rbind,g(g(g(a,b),c),d)) 

and on.