permutation cycle writer notation start
Basically like jo'i, but for cycles. Use boi in order to separate terms. Terminated by tei'u. In this notation, each term maps to the the subsequent term as read from left to right or heard in chronological order of utterance; the last term (immediately before tei'u) maps to the first term. The object constructed is a cyclic permutation, a group element. The singleton cycle is identity on that term. It can be applied to a single element among its terms or may left group act upon a set or structure, or an element if the application is not directly upon it (such as when the application is to an index or variable of that element). Permutations are composed when viewed from outside of their group structure and have the group operator act upon them when within that context. The transposition (1 2) is expressed as ' li ja'oi pa boi re tei'u '. See also: tei'u, ma'o'e, gu'ai, ru'ei, fa'ai.