Etymology
Advertisement
permutation (n.)

late 14c., permutacioun, "interchange, concurrent change; exchange of one thing, position, condition, etc., for another," from Old French permutacion "change, shift" (14c.), from Latin permutationem (nominative permutatio) "a change, alteration, revolution," noun of action from past participle stem of permutare "change thoroughly, exchange," from per "thoroughly" (see per) + mutare "to change" (from PIE root *mei- (1) "to change, go, move"). The sense of "a linear arrangement of objects resulting from a change of their order" is by 1710, originally in mathematics.

Permutation differs from combination in this, that in the latter there is no reference to the order in which the quantities are combined, whereas in the former this order is considered, and consequently the number of permutations always exceeds the number of combinations. [Century Dictionary]
Related entries & more 
Advertisement
transmutation (n.)

late 14c., from Old French transmutacion "transformation, change, metamorphosis" (12c.), from Late Latin transmutationem (nominative transmutatio) "a change, shift," noun of action from past-participle stem of Latin transmutare "change from one condition to another," from trans "across, beyond; thoroughly" (see trans-) + mutare "to change" (from PIE root *mei- (1) "to change, go, move"). A word from alchemy.

Related entries & more 
variant (adj.)
late 14c., "tending to change," from Old French variant and directly from Latin variantem (nominative varians), present participle of variare "to change" (see vary).
Related entries & more 
transform (v.)
Origin and meaning of transform

mid-14c., "change the form of" (transitive), from Old French transformer (14c.), from Latin transformare "change in shape, metamorphose," from trans "across, beyond" (see trans-) + formare "to form" (see form (v.)). Intransitive sense "undergo a change of form" is from 1590s. Related: Transformed; transforming.

Related entries & more 
revolutionize (v.)

1797, "to cause (a state, etc.) to undergo a (political) revolution, effect a change in the political constitution of;" see revolution + -ize. Transferred sense of "change a thing completely and fundamentally, effect radical change in" is by 1799. Related: Revolutionized; revolutionizing.

Related entries & more 
Advertisement
alteration (n.)

late 14c., alteracioun, "change, transformation, action of altering," from Old French alteracion "change, alteration" (14c.), and directly from Medieval Latin alterationem (nominative alteratio), noun of action from past-participle stem of Late Latin alterare "to change," from Latin alter "the other (of the two)," from PIE root *al- (1) "beyond" + comparative suffix -ter (as in other). Meaning "change in character or appearance" is from 1530s; that of "change in ready-made clothes to suit a customer's specifications" is from 1901. Related: Alterations.

Related entries & more 
variance (n.)
late 14c., "fact of undergoing change," from Old French variance "change, alteration; doubt, hesitation" and directly from Latin variantia, from stem of variare "to change" (see vary). Meaning "state of disagreement" is recorded from early 15c. The U.S. zoning sense of "official dispensation from a building regulation" is recorded from 1925.
Related entries & more 
permutate (v.)

1898 in the modern sense of "change the order of" (earlier "to change, alter, 16c. but obsolete thereafter), from Latin permutatus, past participle of permutare "change thoroughly, exchange" (see permutation). "Probably regarded by those who use it as a back-formation from permutation" [OED]. Compare permute. Related: Permutated; permutating.

Related entries & more 
transmute (v.)
late 14c., "transform the appearance of," from Latin transmutare "change from one condition to another," from trans "across, beyond; thoroughly" (see trans-) + mutare "to change" (from PIE root *mei- (1) "to change, go, move"). Related: Transmuted; transmuting.
Related entries & more 
alter (v.)

late 14c., "to change (something), make different in some way," from Old French alterer "to change, alter," from Medieval Latin alterare "to change," from Latin alter "the other (of the two)," from PIE root *al- (1) "beyond" + comparative suffix -ter (as in other). Intransitive sense "to become otherwise" first recorded 1580s. Related: Altered; altering.

Related entries & more 

Page 3