All rune sequences that we deal with this Dynasty are likely to be finite in length, so I think we can agree that it will be unnecessary to ever specify “finite sequence” from here on.  We will, however, be needing to refer to one sequence being “inside” another, and the simplest way of doing this is to borrow the terminology of “subsequence”.  A sequence is just a set (that’s allowed to have repeating runes) that has an order.  So a subsequence just means any subset that has the same relative order.

Original sequence:  PROSTAXUP

Example subsequences:  PUP, ROT, PROSTAXUP, TAX, PP

Not subsequences:  ROAST (the A is out of order), SS (there aren’t 2 copies of S in the original sequence), SORP (it appears backwards in the original, but that doesn’t count)

This notion of subsequence does not inherently carry any assumption that the subsequence appears _consecutively_ in the original sequence, but it’s simple enough to just say “consecutive subsequence” if that’s what you mean.  If that’s too cumbersome, I suggest defining “subword” or similar to mean just that.

I think it’s perfectly fine to have a mixture of consecutive and not-necessarily-consecutive requirements for various things.  Consecutive requirements can lead to more powerful effects, for example, since they’re harder to assemble.  Non-consecutive requirements could also be interesting, since a clever player might be able to have several options available at once, without committing to any of them.

For now, I’m just wondering what people have been assuming when they write proposals (or vote on proposals), so I can make a reasonable proposal with definitions, and which doesn’t mess up anyone’s intent.  In particular:

*Kevan’s amulets proposal specifies a group from “either the start or the end” and “in the same order”, so it’s clear what e intended.
*My SAP and SORT rule looks for not-necessarily-consecutive runes, but the effect of SAP is not very powerful, and SORT is only somewhat powerful and requires 4 out of 5 workbench slots to pull off (which probably makes you an appealing SAP target).  But I don’t mind changing it if there are a bunch of you who assumed I meant consecutive, and would have voted AGAINST had you known.
*Bucky has a spellcasting draft that just says “subsequence”, which I think is good, and leaves the door open for some spells (maybe even a majority) that specifically require consecutive subsequences.
*spikebrennan has told me that he meant only for consecutive “AAOO” or “AOOA” to be able to change into “UUUU” in eir unstable runes proposal.