Permuted, meaning "to change the order or arrangement of something," has several synonyms that can be used interchangeably in different contexts. One synonym is "rearranged," which implies a new order or placement of items. Another synonym is "shuffled," which suggests a random or haphazard rearrangement. "Transposed" is another synonym, indicating a switch or exchange of positions. "Swapped" is another option, meaning a direct exchange of positions between two elements. Lastly, "interchanged" implies a mutual exchange or substitution, and "mutated" suggests a more drastic change, often used in scientific or genetic contexts. All these words can replace "permuted" depending on the intended tone and context.