A "matching problem"

vector1 <- sample(LETTERS[1:6]) # randomize
vector2 <- letters[1:6]
# convert to lower case for matching
vector1 <- tolower(vector1)
vector2 <- tolower(vector2)
# count the number of matches so order does not matter
count <- match(vector1, vector2)
if (length(count[!is.na(count)]) == length(vector1)) print("match") else print('no match')

vector1 <- sample(letters, 6)
vector1

count <- match(vector1, vector2)
if (length(count[!is.na(count)]) == length(vector1)) print("match") else print('no match')

Dear all, I was encountering with a typical Matching problem and was
wondering whether R can help me to solve it directly.

Let say, I have 2 vectors of equal length:
vector1 <- LETTERS[1:6]
vector2 <- letters[1:6]

Now I need to match these 2 vectors with all possible ways like:

(A,B,C,D,E) & (a,b,c,d,e) is 1 match. Another match can be (A,B,C,D,E) &
(b,a,c,d,e), however there cant be any duplication.

Is there any direct way to doing that in R?

Thanks and regards,