2,272 research outputs found
Wreath Products of Permutation Classes
A permutation class which is closed under pattern involvement may be
described in terms of its basis. The wreath product construction X \wr Y of two
permutation classes X and Y is also closed, and we investigate classes Y with
the property that, for any finitely based class X, the wreath product X \wr Y
is also finitely based.Comment: 14 page
Elementary amenable subgroups of R. Thompson's group F
The subgroup structure of Thompson's group F is not yet fully understood. The
group F is a subgroup of the group PL(I) of orientation preserving, piecewise
linear self homeomorphisms of the unit interval and this larger group thus also
has a poorly understood subgroup structure. It is reasonable to guess that F is
the "only" subgroup of PL(I) that is not elementary amenable. In this paper, we
explore the complexity of the elementary amenable subgroups of F in an attempt
to understand the boundary between the elementary amenable subgroups and the
non-elementary amenable. We construct an example of an elementary amenable
subgroup up to class (height) omega squared, where omega is the first infinite
ordinal.Comment: 20 page
The orbifold transform and its applications
We discuss the notion of the orbifold transform, and illustrate it on simple
examples. The basic properties of the transform are presented, including
transitivity and the exponential formula for symmetric products. The connection
with the theory of permutation orbifolds is addressed, and the general results
illustrated on the example of torus partition functions
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