Semi-pointed partition posets and Species

We define semi-pointed partition posets, which are a generalisation of partition posets and show that they are Cohen-Macaulay. We then use multichains to compute the dimension and the character for the action of the symmetric groups on their homology. We finally study the associated incidence Hopf algebra, which is similar to the Fa{\`a} di Bruno Hopf algebra.Comment: 27 page

Hypertree posets and hooked partitions

We adapt here the computation of characters on incidence Hopf algebras introduced by W. Schmitt in the 1990s to a family mixing bounded and unbounded posets. We then apply our results to the family of hypertree posets and partition posets. As a consequence, we obtain some enumerative formulas and a new proof for the computation of the Moebius numbers of the hypertree posets. Moreover, we compute the coproduct of the incidence Hopf algebra and recover a known formula for the number of hypertrees with fixed valency set and edge sizes set.Comment: 18 page

Decorated hypertrees

C. Jensen, J. McCammond and J. Meier have used weighted hypertrees to compute the Euler characteristic of a subgroup of the automorphism group of a free product. Weighted hypertrees also appear in the study of the homology of the hypertree poset. We link them to decorated hypertrees after a general study on decorated hypertrees, which we enumerate using box trees.---C. Jensen, J. McCammond et J. Meier ont utilis\'e des hyperarbres pond\'er\'es pour calculer la caract\'eristique d'Euler d'un sous-groupe du groupe des automorphismes d'un produit libre. Un autre type d'hyperarbres pond\'er\'es appara\^it aussi dans l'\'etude de l'homologie du poset des hyperarbres. Nous \'etudions les hyperarbres d\'ecor\'es puis les comptons \`a l'aide de la notion d'arbre en bo\^ite avant de les relier aux hyperarbres pond\'er\'es.Comment: nombre de pages : 3

Voltaire's "Racine": the paradoxes of a transformation

This article highlights some paradoxical aspects of Voltaire's admiration for Racine. He paid little attention to Racine's plays as dramatic entities, followed received opinions, and made many unfavourable judgements, especially concerning Racine's mix of tragedy and galanterie. What he idolized was Racine's use of language and his poetic skill. He thus removed Racine's tragedies from the contingencies of the theatre, and transformed them into an eighteenth-century linguistic and cultural ideal that he used for polemical purposes in a war against Shakespeare and encroaching barbarism, leading the Romantics subsequently to reject the `Racine' he had been so influential in creating

‘The rhetoric of space and self in Racine’s Bérénice’

This essay explores the ways in which Racine defines the physical and conceptual spaces which his characters inhabit in Bérénice, and illustrates the semantic complexity of some of the play’s principal terms

La Lettre performative. Quand dire, c’est faire chez Racine

La théorie du performatif élaborée par Austin comprend deux éléments qui s'appliquent au théâtre de Racine : la notion de performance (elle-même théâtrale), et l'importance de la première personne qui, selon Benveniste, crée l'espace de l'énonciation. Une discussion de cette théorie appliquée au théâtre tragique - où les personnages tragiques sont souvent « parlés » plutôt que « parlants », et où le langage tragique joue avec eux davantage qu'eux avec lui - est suivie d'une analyse de Bérénice et de Bajazet et de quelques commentaires sur Andromaque et Phèdre.Austin's theory of the performative includes two elements applicable to Racine's plays: the notion of performance, which is itself theatrical, and the importance of the first person which, according to Benveniste, creates the space of enunciation. A discussion of the applicability of this theory to tragedy-in which characters are often "spoken" rather than "speaking", with tragic language playing with them rather than they with it-is followed by an analysis of Bérénice and Bajazet, and a few comments about Andromaque and Phèdre