45,779 research outputs found
New moduli spaces of pointed curves and pencils of flat connections
It is well known that formal solutions to the Associativity Equations are the
same as cyclic algebras over the homology operad of
the moduli spaces of --pointed stable curves of genus zero. In this paper we
establish a similar relationship between the pencils of formal flat connections
(or solutions to the Commutativity Equations) and homology of a new series
of pointed stable curves of genus zero. Whereas
parametrizes trees of 's with pairwise distinct nonsingular marked
points, parametrizes strings of 's stabilized by marked
points of two types. The union of all 's forms a semigroup rather
than operad, and the role of operadic algebras is taken over by the
representations of the appropriately twisted homology algebra of this union.Comment: 37 pages, AMSTex. Several typos corrected, a reference added,
subsection 3.2.2 revised, subsection 3.2.4 adde
Varieties of Cost Functions.
Regular cost functions were introduced as a quantitative generalisation of regular languages, retaining many of their equivalent characterisations and decidability properties. For instance, stabilisation monoids play the same role for cost functions as monoids do for regular languages. The purpose of this article is to further extend this algebraic approach by generalising two results on regular languages to cost functions: Eilenberg's varieties theorem and profinite equational characterisations of lattices of regular languages. This opens interesting new perspectives, but the specificities of cost functions introduce difficulties that prevent these generalisations to be straightforward. In contrast, although syntactic algebras can be defined for formal power series over a commutative ring, no such notion is known for series over semirings and in particular over the tropical semiring
Characterization of Multivariate Permutation Polynomials in Positive Characteristic
Multivariate permutation polynomials over the algebra of formal series over a finite field and its residual algebras are characterized. Some known properties of permutation polynomials over finite fields are also extended.AMS Classification 2000: 13B25, 13F25, 11T55. Keywords: Multivariate permutation polynomials.
Groups of tree-expanded series
We describe the proalgebraic groups represented by three Hopf algebras on
planar binary trees previously introduced by the author and Christian Brouder
in relation with the renormalization of quantum electrodynamics. Using two
monoidal structures and a set-operad structure on planar binary trees, we show
that these groups can be realized on formal series expanded over trees, and
that the group laws are generalization of the multiplication and the
composition of usual series in one variable. All the constructions are done in
a general operad-theoretic setting, and then applied to the duplicial operad on
trees.Comment: 30 pages; added references, to appear in J.Algebr
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