Transposition

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A transposition in chess is a sequence of moves that results in a position which may also be reached by another sequence of moves. For instance 1. d4 e6 2. e4 versus 1. e4 e6 2. d4, or {6. cxd4 exd4 7. exd4} versus {6. exd4 exd4 7. cxd4}. At least two moves (three plies) are necessary to transpose by exchanging moves, the more plies, the more possible sequences with transpositions are possible.

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Different Number of Moves

Due to both sides may lose tempo, more or less forced but often plausible transpositions with different number of moves may occur. A common example is this position from the [https://en.wikipedia.org/wiki/Sicilian_Defence#Sveshnikov_Variation:_4...Nf6_5.Nc3_e5 Sveshnikov Variation] in the Sicilian, which regularly appears after seven or eight moves:

r1bqkb1r/pp3ppp/2np1n2/1N2p1B1/4P3/2N5/PPP2PPP/R2QKB1R

1. e4 c5 2. Nf3 d6 3. d4 cxd 4. Nxd4 Nf6 5. Nc3 Nc6 6. Bg5 e5 7. Ndb5 1. e4 c5 2. Nc3 e6 3. Nf3 Nc6 4. d4 cxd 5. Nxd4 Nf6 6. Ndb5 d6 7. Bf4 e5 8. Bg5

Color Flip

Further, during the opening, there are zillions of possibilities to transpose into color flipped positions from known opening lines, often by the prosaic loss of a tempo by performing a move, i.e. a double pawn push in two steps, for instance 1. d3 d5 2. d4 to play "Black" with the White pieces, as often tried by humans to throw a program out of its opening book early, but also by programs, like in the WMCCC 1988 the Pandix-Y!88 game. Therefor, books indexed by positions or hash keys may be re-probed with a color flipped position to cover those kinds of transpositions as well:

r1bqkb1r/pp3ppp/2n1pn2/2pp4/4P3/2NP1NP1/PPP2P1P/R1BQKB1R

r1bqkb1r/ppp2p1p/2np1np1/4p3/2PP4/2N1PN2/PP3PPP/R1BQKB1R

1. e4 c5 2. Nc3 Nc6 3. Nf3 e6
4. g3 Nf6 5. d3 d5

1. c4 e5 2. Nc3 Nc6 3. Nf3 d6
4. d3 Nf6 5. e3 g6 6. d4

Retrograde Analysis

In analyzing book lines, Retrograde Analysis from an opening or early middlegame position backwards reaching the initial position might be applied to traverse a "reverse" tree of unmade moves of variations with all its transpositions. However, one has to distinguish possible variations, where for instance pieces were put en prise but not captured, from plausible ones.