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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?

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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
  • Please use only IPA for pronunciations on ELU. – tchrist May 7 '14 at 4:19
  • I copied straight from the dictionary page. – Blessed Geek May 7 '14 at 4:20
  • That is no excuse for using an unusable encoding system. You render your answer completely out of reach of most readers; it is a poor joke perpetrated on credulous Americans, and it does not work. Use IPA or nothing. – tchrist May 7 '14 at 4:21
  • Even though brought up speaking British English, and continue to write in archaic British style, I am American now. If anyone finds us credulous and ineffective, then they should stop using Google, Yahoo, or the IPhone, or even the internet. Stop drinking Coca-cola. Whatever. – Blessed Geek May 7 '14 at 8:20
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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).

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