3,267 research outputs found
Generalized iterated wreath products of symmetric groups and generalized rooted trees correspondence
Consider the generalized iterated wreath product of symmetric groups. We give a complete description of the traversal
for the generalized iterated wreath product. We also prove an existence of a
bijection between the equivalence classes of ordinary irreducible
representations of the generalized iterated wreath product and orbits of labels
on certain rooted trees. We find a recursion for the number of these labels and
the degrees of irreducible representations of the generalized iterated wreath
product. Finally, we give rough upper bound estimates for fast Fourier
transforms.Comment: 18 pages, to appear in Advances in the Mathematical Sciences. arXiv
admin note: text overlap with arXiv:1409.060
Dendriform-Tree Setting for Fully Non-commutative Fliess Operators
This paper provides a dendriform-tree setting for Fliess operators with
matrix-valued inputs. This class of analytic nonlinear input-output systems is
convenient, for example, in quantum control. In particular, a description of
such Fliess operators is provided using planar binary trees. Sufficient
conditions for convergence of the defining series are also given
Simply Generated Trees, B-series and Wigner Processes
We consider simply generated trees and study multiplicative functions on
rooted plane trees. We show that the associated generating functions satisfy
differential equations or difference equations. Our approach considers B-series
from Butcher's theory, the generating functions are seen as generalized
Runge-Kutta methodsComment: 19 pages, 1 figur
Hyperbolic tilings and formal language theory
In this paper, we try to give the appropriate class of languages to which
belong various objects associated with tessellations in the hyperbolic plane.Comment: In Proceedings MCU 2013, arXiv:1309.104
Multiple zeta value cycles in low weight
In a recent work, the author has constructed two families of algebraic cycles
in Bloch cycle algebra over the prjective line minus 3 points that are expected
to correspond to multiple polylogarithms in one variable and have a good
specialization at 1 related to multiple zeta values. This is a short
presentation, by the way of toy examples in low weight (5), of this contruc-
tion and could serve as an introduction to the general setting. Working in low
weight also makes it possible to push ("by hand") the construction further. In
particular, we will not only detail the construction of the cycle but we will
also associate to these cycles explicit elements in the bar construction over
the cycle algebra and make as explicit as possible the "bottow-left"
coefficient of the Hodge realization periods matrix. That is, in a few relevant
cases we will associated to each cycles an integral showing how the
specialization at 1 is related to multiple zeta values. We will be particularly
interested in a new weight 3 example .Comment: revised version
Dendriform Equations
We investigate solutions for a particular class of linear equations in
dendriform algebras. Motivations as well as several applications are provided.
The latter follow naturally from the intimate link between dendriform algebras
and Rota-Baxter operators, e.g. the Riemann integral or Jackson's q-integral.Comment: improved versio
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