permutation has 4 distinct synonyms spread across 1 of its 4 senses. Each sense below keeps its own list, because a synonym belongs to a meaning and not to a word: swapping one sense's substitute into another sense's sentence is how a thesaurus makes writing worse. WordNet records no antonym for it — antonymy is a relation between word forms rather than concepts, so it is deliberately sparse.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
an event in which one thing is substituted for another
“the replacement of lost blood by a transfusion of donor blood”
the act of changing the arrangement of a given number of elements
Synonyms, antonyms and the broader and narrower relations for permutation come from Princeton University’s WordNet. Full sources and licences.
complete change in character or condition
“the permutations...taking place in the physical world”
act of changing the lineal order of objects in a group