Higher order peak algebras

Using the theory of noncommutative symmetric functions, we introduce the higher order peak algebras, a sequence of graded Hopf algebras which contain the descent algebra and the usual peak algebra as initial cases (N = 1 and N = 2). We compute their Hilbert series, introduce and study several combinatorial bases, and establish various algebraic identities related to the multisection of formal power series with noncommutative coefficients.Comment: 20 pages, AMS LaTe

Some consequences of a Fatou property of the tropical semiring

We show in this paper that the tropical semiring (integers equiped with (max,+) operations) has the Fatou property and study the consequences of this property with respect to decidability properties

Modeling Commercial Processes and Customer Behaviors to Estimate

We propose a formal model for estimating the diffusion rate of a new product on a coherent market. Our approach is based on a discrete probabilistic modeling of customer behaviors and of commercial processes.Diffusion of innovation, diffusion rate, marketing, customer behavior, product diffusion

Pareto optimality and Nash equilibrium for building stable systems

This paper introduces a design approach based on system analysis and game theory for the identification of architectural equilibrium which guarantees the stability of the system being designed and its environment after the integration. We introduce multi-objective optimization and game theory, and their links with systems engineering through mathematical models. While Pareto optimality is used to select best architectures and to support independent decisions, Nash equilibrium is used to find out architectural equilibrium and to support interdependent decisions. This approach was illustrated previously in a case study

A combinatorial approach to evaluation of reliability of the receiver output for BPSK modulation with spatial diversity

Article publié en ligne à l'adresse : http://www.combinatorics.org/Volume_13/Abstracts/v13i1r2.htmlA combinatorial approach for computing the Bit Error Ratio of a modulation protocol used in mobile telecommunications is proposed

Performance analysis of modulation with diversity - A combinatorial approach II : Bijective methods

We propose different bijective methods for studying the performance of a modulation protocol with diversity in the context of mobile communications

Noncommutative symmetric functions V : A degenerate version of Uq(GlN )

["Special issue for the memory of M. Schutzenberger", J.E. Pin Ed.]Nous montrons que la théorie des fonctions symétriques non commutatives permet de rendre compte des représentations d'une version dégénérée de la version quantique de l'algèbre enveloppante de GlN