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MR2052167 20F36
Malyutin, A. V.; Netsvetaev, N. Yu. Dehornoy order in the braid group and transformations of closed braids. (Russian) Algebra i Analiz 15 (2003), no. 3, 170--187; translation in St. Petersburg Math. J. 15 (2003), no. 3, 437–448
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