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Conjugacy in Garside Groups III: Periodic braids
An element in Artin's braid group B_n is said to be periodic if some power of
it lies in the center of B_n. In this paper we prove that all previously known
algorithms for solving the conjugacy search problem in B_n are exponential in
the braid index n for the special case of periodic braids. We overcome this
difficulty by putting to work several known isomorphisms between Garside
structures in the braid group B_n and other Garside groups. This allows us to
obtain a polynomial solution to the original problem in the spirit of the
previously known algorithms.
This paper is the third in a series of papers by the same authors about the
conjugacy problem in Garside groups. They have a unified goal: the development
of a polynomial algorithm for the conjugacy decision and search problems in
B_n, which generalizes to other Garside groups whenever possible. It is our
hope that the methods introduced here will allow the generalization of the
results in this paper to all Artin-Tits groups of spherical type.Comment: 33 pages, 13 figures. Classical references implying Corollaries 12
and 15 have been added. To appear in Journal of Algebr
Upper bound on the characters of the symmetric groups for balanced Young diagrams and a generalized Frobenius formula
We study asymptotics of an irreducible representation of the symmetric group Sn corresponding to a balanced Young diagram λ (a Young diagram with at most View the MathML source rows and columns for some fixed constant C) in the limit as n tends to infinity
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