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On the string of finite length, a (genomic) transposition is defined as theoperation of exchanging two consecutive substrings. The minimum number oftranspositions needed to transform one into the other is the transpositiondistance, that has been researched in recent years. In this paper, we studytransposition distances on circular binary strings. A circular binary string isthe string that consists of symbols $0$ and $1$ and regards its circular shiftsas equivalent. The property of transpositions which partition strings isobserved. A lower bound on the transposition distance is represented in termsof partitions. An upper bound on the transposition distance follows covering ofthe set of partitions. The transposition diameter is given with a necessary andsufficient condition.

Transposition diameter on circular binary strings