Lattice Diagram polynomials in one set of variables

The space $M_{\mu/i,j}$ spanned by all partial derivatives of the lattice polynomial $\Delta_{\mu/i,j}(X;Y)$ is investigated in math.CO/9809126 and many conjectures are given. Here, we prove all these conjectures for the $Y$-free component $M_{\mu/i,j}^0$ of $M_{\mu/i,j}$. In particular, we give an explicit bases for $M_{\mu/i,j}^0$ which allow us to prove directly the central {\sl four term recurrence} for these spaces.Comment: 15 page

The symmetric operation in a free pre-Lie algebra is magmatic

A pre-Lie product is a binary operation whose associator is symmetric in the last two variables. As a consequence its antisymmetrization is a Lie bracket. In this paper we study the symmetrization of the pre-Lie product. We show that it does not satisfy any other universal relation than commutativity. It means that the map from the free commutative-magmatic algebra to the free pre-Lie algebra induced by the symmetrization of the pre-Lie product is injective. This result is in contrast with the associative case, where the symmetrization gives rise to the notion of Jordan algebra. We first give a self-contained proof. Then we give a proof which uses the properties of dendriform and duplicial algebras.Comment: View in color, 12 page

Un cadre théorique pour l’étude de la relation entre la participation et la motivation au travail

À la suite d'une description des différentes théories qui ont été avancées pour expliquer une relation possible entre la participation et la motivation, l'auteur soutient que ces théories pèchent souvent sur deux points majeurs: une définition trop vague de ce qu'est la participation et l'absence d'un modèle explicite de motivation au travail. Il s'attache donc à corriger ces déficiences et à démontrer par quels processus certaines formes de participation peuvent affecter chacune des trois composantes du modèle VIE (Expectancy) de motivation. La capacité que semble posséder ce modèle d'intégrer toutes les théories présentées au début de l'article fait ensuite l'objet d'une brève discussion.For a great number of authors and for some administrators, it is "obvious" that participation leads to employee motivation. What is less obvious, however, is the reason (or set of reasons) why this should be so. Several theories or explanations have been put forward in the literature, and seven of them are summarized here, including the assumed influence of participation on ego-involvement, on self-esteem, on group norms and group pressure for conformity, on organizational identification. It is found, however, that several of these explanations lack both a clear definition of participation and a conceptual framework or theory of motivation.In this article, participation is defined as "perceived influence" and a distinction is made between three objets of this influence: the job (methods and goals), the immediate superior, the organization. Influence exerted through group decision-making is considered to be a fourth type of participation. The expectancy or VIE model of work motivation is adopted as a general framework, in spite of its numerous ambiguities and possible shortcomings.The processes and various intervening variables through which the four types of participation might affect expectancy, instrumentality, and "valence" are then examined in some detail. It is argued, for instance, that participation in the sense of influence on one's job might increase expectancy through its effects on goal clarity, goal accessibility, goal acceptance, and job-related self-esteem. The same type of participation may also influence the instrumentality of high performance for feelings of achievement through its effect on ego-involvement. Influence on one's superior may increase the instrumentality of high performance for feelings of equity through a process of "exchange", described by Jacobs (1971). Influence on both the superior and the organization may increase instrumentality by allowing the employee some control over the application of the organization's reward policies. Finally, participation in the form of group decision-making may clarify the group norms and induce the employee to believe that high performance will be followed by group acceptance (if group norms happen to be high). As far as "valence" is concerned, participation (influence oh one's job) may increase the employee's need for achievement-related outcomes. Influence on the organization may affect "valence" by increasing the employee's identification with the organization and therefore the valence of organization-supporting outcomes such as organization success and reputation. The same type of influence may allow the employee to determine some of the consequences of good performance or to select those he likes best, thereby increasing the valence of these consequences. Finally, group decision-making could increase the group's cohesion and value to the employee and consequently the valence of group approval.The value of the model presented here lies partly in the fact that it can integrate all the theories or explanations presented by other authors (summarized at the beginning of the article) to justify a possible link between participation and motivation. Vroom's argument about ego-involvement, for instance, is used here to explain a possible relationship between participation and instrumentality.Although the purpose of this article is to present a conceptual framework and not to test its validity, some empirical results have been obtained which suggest that certain parts of the model may indeed be valid. One shortcoming of the model, however, is that it does not include the numerous moderating variables which undoubtedly affect most of the hypothesized relationships. Like all models, it depicts only a small part of a complex reality