"Permuter" is a word in ENGLISH

permuter ENGLISH
Definition:

One who permutes.

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ablaut ENGLISH

The substitution of one root vowel for another, thus indicating a corresponding modification of use or meaning; vowel permutation; as, …

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permutation ENGLISH

Any one of such possible arrangements.

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permutation ENGLISH

The arrangement of any determinate number of things, as units, objects, letters, etc., in all possible orders, one after the …

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Permutation LAW AND LEGAL

The exchange of one movable subject for another; barter

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