Orderings on braid groups, operations on closed braids, and confirmation of Menasco's conjectures
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 5, Tome 267 (2000), pp. 163-169

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Conditions are described necessary for certain operations on closed braids to be admissible. Menasco's conjectures are proved as a corollary.
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     author = {A. V. Malyutin},
     title = {Orderings on braid groups, operations on closed braids, and confirmation of {Menasco's} conjectures},
     journal = {Zapiski Nauchnykh Seminarov POMI},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2000_267_a11/}
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A. V. Malyutin. Orderings on braid groups, operations on closed braids, and confirmation of Menasco's conjectures. Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 5, Tome 267 (2000), pp. 163-169. http://geodesic.mathdoc.fr/item/ZNSL_2000_267_a11/