Unique combination of all elements from two (or more) vectors

this maybe what you are after

> expand.grid(a,b)
   Var1       Var2
1   ABC 2012-05-01
2   DEF 2012-05-01
3   GHI 2012-05-01
4   ABC 2012-05-02
5   DEF 2012-05-02
6   GHI 2012-05-02
7   ABC 2012-05-03
8   DEF 2012-05-03
9   GHI 2012-05-03
10  ABC 2012-05-04
11  DEF 2012-05-04
12  GHI 2012-05-04
13  ABC 2012-05-05
14  DEF 2012-05-05
15  GHI 2012-05-05

If the resulting order isn't what you want, you can sort afterwards. If you name the arguments to expand.grid, they will become column names:

df = expand.grid(a = a, b = b)
df[order(df$a), ]

And expand.grid generalizes to any number of input columns.

The tidyr package provides the nice alternative crossing, which works better than the classic expand.grid function because (1) strings are not converted into factors and (2) the sorting is more intuitive:

library(tidyr)

a <- c("ABC", "DEF", "GHI")
b <- c("2012-05-01", "2012-05-02", "2012-05-03", "2012-05-04", "2012-05-05")

crossing(a, b)

# A tibble: 15 x 2
       a          b
   <chr>      <chr>
 1   ABC 2012-05-01
 2   ABC 2012-05-02
 3   ABC 2012-05-03
 4   ABC 2012-05-04
 5   ABC 2012-05-05
 6   DEF 2012-05-01
 7   DEF 2012-05-02
 8   DEF 2012-05-03
 9   DEF 2012-05-04
10   DEF 2012-05-05
11   GHI 2012-05-01
12   GHI 2012-05-02
13   GHI 2012-05-03
14   GHI 2012-05-04
15   GHI 2012-05-05

Missing in this r-faq overview is the CJ-function from the data.table-package. Using:

library(data.table)
CJ(a, b, unique = TRUE)

gives:

a b 1: ABC 2012-05-01 2: ABC 2012-05-02 3: ABC 2012-05-03 4: ABC 2012-05-04 5: ABC 2012-05-05 6: DEF 2012-05-01 7: DEF 2012-05-02 8: DEF 2012-05-03 9: DEF 2012-05-04 10: DEF 2012-05-05 11: GHI 2012-05-01 12: GHI 2012-05-02 13: GHI 2012-05-03 14: GHI 2012-05-04 15: GHI 2012-05-05

_{NOTE: since version 1.12.2 CJ autonames the resulting columns (see also here and here).}

Since version 1.0.0, tidyr offers its own version of expand.grid(). It completes the existing family of expand(), nesting(), and crossing() with a low-level function that works with vectors.

When compared to base::expand.grid():

Varies the first element fastest. Never converts strings to factors. Does not add any additional attributes. Returns a tibble, not a data frame. Can expand any generalised vector, including data frames.

a <- c("ABC", "DEF", "GHI")
b <- c("2012-05-01", "2012-05-02", "2012-05-03", "2012-05-04", "2012-05-05")

tidyr::expand_grid(a, b)

   a     b         
   <chr> <chr>     
 1 ABC   2012-05-01
 2 ABC   2012-05-02
 3 ABC   2012-05-03
 4 ABC   2012-05-04
 5 ABC   2012-05-05
 6 DEF   2012-05-01
 7 DEF   2012-05-02
 8 DEF   2012-05-03
 9 DEF   2012-05-04
10 DEF   2012-05-05
11 GHI   2012-05-01
12 GHI   2012-05-02
13 GHI   2012-05-03
14 GHI   2012-05-04
15 GHI   2012-05-05

you can use order function for sorting any number of columns. for your example

df <- expand.grid(a,b)
> df
   Var1       Var2
1   ABC 2012-05-01
2   DEF 2012-05-01
3   GHI 2012-05-01
4   ABC 2012-05-02
5   DEF 2012-05-02
6   GHI 2012-05-02
7   ABC 2012-05-03
8   DEF 2012-05-03
9   GHI 2012-05-03
10  ABC 2012-05-04
11  DEF 2012-05-04
12  GHI 2012-05-04
13  ABC 2012-05-05
14  DEF 2012-05-05
15  GHI 2012-05-05

> df[order( df[,1], df[,2] ),] 
   Var1       Var2
1   ABC 2012-05-01
4   ABC 2012-05-02
7   ABC 2012-05-03
10  ABC 2012-05-04
13  ABC 2012-05-05
2   DEF 2012-05-01
5   DEF 2012-05-02
8   DEF 2012-05-03
11  DEF 2012-05-04
14  DEF 2012-05-05
3   GHI 2012-05-01
6   GHI 2012-05-02
9   GHI 2012-05-03
12  GHI 2012-05-04
15  GHI 2012-05-05`