A word that means "dependent on the order of items"

Question

I'm trying to find a word that means "dependent on the order of items".

For example, the list of letters "ABCDEF" and "FEDCBA" contain the same letters. If order is NOT considered, both lists contain the same letters. If order IS considered, the two lists are different.

What word indicates that the order of letters must be taken into account when comparing the lists?

Clarification: The context is computer science. I'm attempting to explain hashing functions. A most basic hash function could simply sum the values of all bytes in the input stream. But this would allow inputs containing the same bytes, regardless of order, to produce equivalent hashes. The next step toward improving the function would be to apply a weight to each position in the input stream, making the resulting hash _______. This is the word I'm looking for, and means "dependent on the order" of the bytes rather than "order-independent". Hope this helps to clarify.

See this conversation.

Answer 1

The word you are looking for is sequence:

Definition of sequence (Merriam-Webster), specifically 2(d) and 3(a) excerpted below:

2: a continuous or connected series: d : a set of elements ordered so that they can be labeled with the positive integers

3: a : order of succession

Then you may compare sequenced lists where order matters, and unsequenced lists where it doesn't.

Answer 2

I think the simple phrase "ordered list" will be clear and accurate, especially in a CS context

Answer 3

Give your context and audience, I think you might be able to use the terms "transposition-dependent" and "transposition-independent" to describe a hash-function that does or does not vary according to order of digits in the original. A less technical audience will probably need the term explained, but I get the impression from your example this will not be needed. Your example becomes:

The next step toward improving the function would be to apply a weight to each position in the input stream, making the resulting hash transposition-dependent.

In this case, I am using defintion 2b of transposition at Merriam-Webster:

a mathematical permutation or interchange of two letters or symbols

Meaning two things got switched within an ordered list of things. If I sepll soem wrods in tihs sentnece incorerctly, then I am making "transposition errors," and it seems you want a hash that will detect these errors. Such a hash will be transposition-dependent.

I mentioned in a comment the check-digit of the International Standard Book Number (ISBN). The function used here does almost exactly what you describe, it multiplies each digit by its place in order, then sums them, then mods. This system was devised exactly to detect both off-by-one errors (i.e. 12345 versus 12445) and transposition errors (i.e. 12345 versus 12435).

Thus the check-digit is transposition-dependent. Note that only taking the sum, without multiplying the weight, would make the check-digit transposition-independent.