Pasting elements of two vectors alphabetically

slightly redundant because it sorts twice, but vectorised,

paste(pmin(a,b), pmax(a,b))

Edit: alternative with ifelse,

ifelse(a < b, paste(a, b), paste(b, a))

Here's one approach:

apply(cbind(a, b), 1, function(x) paste(sort(x), collapse=" "))

## [1] "george harry" "harry steve"  "chris harry"  "chris harry"  
## [5] "harry steve" "george steve" "chris steve"  "george harry"

Using your initial attempt, you could also do the following but they both require more typing (not sure about speed):

unlist(Map(function(x, y) paste(sort(c(x, y)), collapse=" "), a, b),,FALSE)
mapply(function(x, y) paste(sort(c(x, y)), collapse=" "), a, b, USE.NAMES = FALSE)

One liner from your own code:

apply(data.frame(apply(mapply(c, a, b, USE.NAMES = FALSE),1,paste)),1,function(x) paste(x[1],x[2]))
[1] "george harry" "harry steve"  "harry chris"  "chris harry"  "steve harry"  "steve george" "steve chris"  "harry george"


apply(apply(mapply(c, a, b, USE.NAMES = FALSE),2,sort),1,paste)

     [,1]     [,2]   
[1,] "george" "harry"
[2,] "harry"  "steve"
[3,] "chris"  "harry"
[4,] "chris"  "harry"
[5,] "harry"  "steve"
[6,] "george" "steve"
[7,] "chris"  "steve"
[8,] "george" "harry"