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MR2307359 57M25
Malyutin, A. V. On the number of closed braids obtained as a result of single stabilizations and destabilizations of a closed braid. (Russian) ; translated from Algebra i Analiz 18 (2006), no. 6, 205--218 St. Petersburg Math. J. 18 (2007), no. 6, 1011–1020
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