In music, transposition is moving a note or collection of notes up or down in pitch by a constant interval.
In mathematics, a transposition is a permutation which exchanges two elements and keeps all others fixed. For example (1 3) is a transposition which exchange 1 and 3. A transposition is a cycle of length two.
In cryptography, a transposition is an elementary cryptographic operation somewhat related to the mathematical permutations.
In chess openings, transpositions are ways of reaching the same position from different sequences of moves. Transpositions are particularly common between queen-pawn openings such as the Queen's Gambit and Nimzo Indian Defense.
In genetics, a transposition is a mutation in which a chromosomal segment is transferred to a new position on the same or another chromosome.
In telecommunication, the term transposition has the following meanings:
In data transmission, a transmission defect in which, during one character period, one or more signal elements are changed from one significant condition to the other, and an equal number of elements are changed in the opposite sense.
In outside plant construction, an interchange of spatial positions of the several conductors of a cable between successive concatenated sections.
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It must be noted that the computation saved by a transposition table lookup is not just the evaluation of a single position - if that were the case, it would hardly be worth the effort, since evaluation functions are designed to be very fast anyway.
Thus, transposition table entries for nodes at a lower depth in the game tree are more valuable (since the size of the subtree rooted at such a node is larger) and are therefore given more importance when the table fills up and some entries must be discarded.
In alpha-beta pruning, the search is fastest (in fact, optimal) when the child of a node corresponding to the best move is always considered first.
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