# Word for collection of items implying both uniqueness and order

A set is a collection of unique items; this word has a very specific meaning, implying that there is no particular order to the items (so two boxes of assorted chocolates, regardless of their place in the box, etc.). How can I succinctly refer to a set which does impose an order on the items, which is not implied by any property of those items (for example, alphabetical sorting), where two such collections are the same only if they appear in the same order? Another way of thinking about it is that it is a numbered sequence/list of entries, where no entry is repeated.

It can be a noun, an adjective, past participle or even a very short phrase (or rather, two to three words). I don't think there is a proper word for it, but I specifically do not want to mention a set as it would be misleading; similarly, 'sorted' seems to imply that it happens based on some clue/property of the items, rather than being an arbitrary order.

• @AndyBonner That sounds like an answer. Aug 23, 2021 at 20:29

"Set" has the very specific meaning of an unordered group in mathematics and derived fields. In these contexts, there are also "ordered sets" (though these are usually ordered by a property of the members, which is not the usage you're looking for). But "set" can also be used in more casual contexts for things that have an order: a "set of socket wrenches" is probably ordered by size. In the context of electronic data there is a word for "containing no duplicate entries": "deduplicated," but this does not imply order. Similarly, "ordered" is the best adjective to indicate a collection sorted according to a rule, but it doesn't rule out duplicates. And neither is common usage in general contexts.

It seems to me you're thinking of two different usages. If a collection contains no duplicates, you're simply looking at the collection. If you're comparing two collections and saying they're the same only if they're in the same order, then you're comparing two things.

There may be specialized words in various fields that capture one or more of these connotations, but I don't know of any one word in general usage. Perhaps the closest we can get is that two collections are "identical in composition and order, neither collection containing duplicates."

• identically ordered sets? Aug 23, 2021 at 23:17

### List:

1. a number of connected items or names written or printed consecutively, typically one below the other.

### Array:

1. an ordered series or arrangement. "several arrays of solar panels will help provide power"
• Either of those are generally allowed to contain duplicates. Aug 23, 2021 at 20:30
• Also, in a software engineering context, an array is not necessarily ordered. Aug 23, 2021 at 22:35

I finally figured it out (some time ago, but I doubt anyone will need it...): a ranking. Rankings, while not a mathematical term, imply both a complete linear order and uniqueness of elements.