generate k-ary sequence

Hey all, I want to thanks the people who helped me on the binary sequences. Now, I am in a difficult position to figure out a k-ary sequence. A k-ary sequence is one in which every element is an integer from 0,1,...,k-1. For example,{2,2,0,1,1,3,3,3,2,3} is a 4-ary sequence. The elements in 4-ary sequence are randomly spotted. Therefore, I want to print out all the possible combinations. I am new to the matlab, could anyone help me to figure out how to code this?

[Guillaume]

It's not clear what the inputs are. You want to generate all the possible combinations of what?

[Bear]

I want to input k value, and generate all the possible combinations of k-ary sequence. Such as the 4-ary sequence above there, there are total 1 zero, 2 ones, 3 twos and 4 threes. But their spots in the sequence will be randomly. I want to print out the all the unique combinations of 4-ary sequence.

[Image Analyst]

Do you want to save a combination that does not appear, but that could appear, for example (using 0,1,2,3) you might have a combination of (1,2,3) but you don't have that in the data, or you might have a combination of (3,2,1,1,2,3,3,2) but you don't.

If you're allowing sequences that don't actually occur in the data, how long can these sequences be? Any length from 1 up to the length of the array, or even longer???

Answer 1

[Guillaume]

For reasonably short sequences, use unique and perms (same as for binary sequences):

kseq = [2,2,0,1,1,3,3,3,2,3];
allp = unique(perms(kseq), 'rows')

For long sequences, perms becomes inefficient/unusable. This thread got the code for a more efficient uniqueperms by John D'Errico.

Answer 2

[Star Strider]

This seems to do what you want:

k = 4;
s = perms([0:k-1]);

[Bear]

hey, I do not think this is correct. {2,2,0,1,1,3,3,3,2,3} is a 4-ary sequence. and k=4 at this time, the total number of elements in this sequence is equal to (k*(k+1))/2, which is 10, your output is 4 elements total.

[Star Strider]

Does this do what you want?

len = fix(k*(k+1)/2);
cmbs = nchoosek(len,k);
for k1 = 1:cmbs
    seq(k1,:) = randi([0 k-1], 1, len);
end
sequ = unique(seq,'rows');

[Bear]

I think you are close to right, but as the 4-ary sequence above there, there are total 1 zero, 2 ones, 3 twos and 4 threes. But their spots in the sequence will be randomly. I want to print out the all the unique combinations of 4-ary sequence.

[Star Strider]

There may be as many as 4^10 = 1048576 such unique sequences, so get another several reams of paper and a dozen or more ink or toner cartridges first.

I limited my results to 210 to demonstrate that there were no repeats in that number of sequences.