Word or phrase that describes a group of acronymic initials that can be any order

Question

Typical acronyms represent a phrase with a fixed word order. For example, NATO (North Atlantic Treaty Organization) is not coherent when reordered to, say, ATNO (Atlantic Treaty North Organization).

Yet a form of 'anagrammatic acronyms' exists where each word stands alone and can be represented in any order (although by convention, one order may be culturally dominant):

• Big five personality traits as OCEAN, NEOAC, CANOE, etc;
• The elements of art as SFTSLVC, TFCSSVL, etc;
• The fire triangle as OHF, HFO, etc.

What do linguists call a collection of word initials that may not mnemonic and can be in any order that pleases the reader or author?

Answer 1

Commutative = where changing the order of words or item would not affect the outcome or meaning of the phrase or equation.

Commutative, as applied to a binary operation, by extension of logic and grouping would apply to triplets, quadruplets, ... and n-tuplets as well. For example, hierarchical commutation of pairs
((a . b) . c) = ((a . c) . b) = ((c . b) . a) = (a . b . c) = (c . a . b), etc.

com•mu•ta•tive (kŏm′yə-tā′tĭv, kə-myo̅o̅′tə-tĭv)
adj.

1. Relating to, involving, or characterized by substitution, interchange, or exchange.
2. Independent of order. Used of a logical or mathematical operation that combines objects or sets of objects two at a time. If a × b = b × a, the operation indicated by × is commutative.

com•mu′ta•tiv′i•ty (kə-myo̅o̅′tə-tĭv′ĭ-tē) n.

commutative (kəˈmjuːtətɪv; ˈkɒmjʊˌteɪtɪv)
adj

1. relating to or involving substitution
2. (Mathematics) maths logic a. (of an operator) giving the same result irrespective of the order of the arguments; thus disjunction and addition are commutative but implication and subtraction are not b. relating to this property: the commutative law of addition.
3. (Logic) maths logic a. (of an operator) giving the same result irrespective of the order of the arguments; thus disjunction and addition are commutative but implication and subtraction are not b. relating to this property: the commutative law of addition. comˈmutatively adv

For example, commutative grammar of certain synthetic languages, where English have scantly such properties.

• She loved him
• She him loved
• Loved him she
• Loved she him
• Him she loved
• Him loved she

Answer 2

If I was more of a linguist, I suppose I'd have to scratch my first impulse to call it an 'incoherent jumble'.

To be a little more serious: if the letters can appear in any order, it is no longer an acronym but an initialism (particularly if the combination is not readily pronounceable).