permutation (English)

Where does "permutation" come from?

The English noun 'permutation' traces its lineage through Middle English 'permutacioun' and Old French 'permutacïon'[1], deriving ultimately from the Medieval Latin accusative form 'permūtātiōnem'[1]. This Latin noun springs from 'permūtō'[6], which combines the prefix 'per-' meaning 'through, along' with 'mūtō' meaning 'change or alter'[3]. Further back, the Latin verb 'muto' descends from the Proto-Indo-European root '*meyth₂-' meaning 'to exchange'[4]. Morphologically in English, the word is also formed from 'permute' combined with the suffix '-ation'[1].

Open questions

The Proto-Indo-European root '*meyth₂-' is possibly derived from '*mey-' and is also reconstructed as '*h₂mey-'. [5]

Full etymology tree

permutation (English), 'One of the ways something exists, or the ways a set of objects can be ordered.'
- inherited permutacioun (Middle English)
  - borrowed permutacïon (Old French)
  - borrowed permutationem (Latin), 'accusative singular of permūtātiō'
    - derived permutatio (Latin), 'change, alteration'
      - derived permuto (Latin), 'to change or alter throughout or completely, transform'
        compound per- (Latin), 'Used to make adjectives or verbs that are "very" something.'
        compound muto (Latin), 'to move, remove'
        derived *meyth₂- (Proto-Indo-European), 'to change'
        derived *mey- (Proto-Indo-European), 'to strengthen'
      - suffix -tio (Latin), '-tion, -ation, -ing; suffixed to verbs to form action nouns denoting a process, action, or result of an action.'

Ancestors

permutationem (Latin)
permute (English)

Descendants and derived words

multipermutation (English)
permutational (English)
permutation box (English)
permutation group (English)
permutation lock (English)
simsun permutation (English)
subpermutation (English)
superpermutation (English)
vexillary permutation (English)

Sources

Updated September 2026

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Etymology data from Wiktionary, CC BY-SA 4.0 · About Miraris