Stammering tableaux

The PASEP (Partially Asymmetric Simple Exclusion Process) is a probabilistic model of moving particles, which is of great interest in combinatorics, since it appeared that its partition function counts some tableaux. These tableaux have several variants such as permutations tableaux, alternative tableaux, tree- like tableaux, Dyck tableaux, etc. We introduce in this context certain excursions in Young's lattice, that we call stammering tableaux (by analogy with oscillating tableaux, vacillating tableaux, hesitating tableaux). Some natural bijections make a link with rook placements in a double staircase, chains of Dyck paths obtained by successive addition of ribbons, Laguerre histories, Dyck tableaux, etc.Comment: Clarification and better exposition thanks reviewer's report

Shadows in Coxeter groups

For a given $w$ in a Coxeter group $W$ the elements $u$ smaller than $w$ in Bruhat order can be seen as the end-alcoves of stammering galleries of type $w$ in the Coxeter complex $\Sigma$. We generalize this notion and consider sets of end-alcoves of galleries that are positively folded with respect to certain orientation $\phi$ of $\Sigma$. We call these sets shadows. Positively folded galleries are closely related to the geometric study of affine Deligne-Lusztig varieties, MV polytopes, Hall-Littlewood polynomials and many more agebraic structures. In this paper we will introduce various notions of orientations and hence shadows and study some of their algorithmic properties.Comment: 30 pages, 8 figures, revised and final versio

Shadows in Coxeter Groups

For a given w in a Coxeter group W, the elements u smaller than w in Bruhat order can be seen as the end alcoves of stammering galleries of type w in the Coxeter complex Σ. We generalize this notion and consider sets of end alcoves of galleries that are positively folded with respect to certain orientation φ of Σ.We call these sets shadows. Positively folded galleries are closely related to the geometric study of affine Deligne–Lusztig varieties, MV polytopes, Hall–Littlewood polynomials, and many more algebraic structures. In this paper, we will introduce various notions of orientations and hence shadows and study some of their algorithmic properties

Recréations ou récréations ? Bégaiements de l’art moderne : reconstitutions, reprises et imitations d’expositions (2010-2013)

De nouveaux paradigmes modifient considérablement les dispositifs expographiques au sein des musées d’art moderne et contemporain, à la faveur de la relecture autocritique et dynamique que ces derniers font de leurs collections et d’une histoire de l’art du vingtième siècle dont ils ont naguère fixé et figé des jalons aujourd’hui largement remis en cause. Des reconstitutions et reprises d’expositions se multiplient, explorant des voies différentes : plusieurs cas de figures peuvent être distingués. Le registre de l’autocélébration, à l’occasion de centenaires (du Sonderbund de Cologne à l’Armory Show de New York) ou de biennales (Venise), fait varier le bégaiement de l’histoire – œuvres absentes, documentées, salles gigognes démembrées ou déplacées, accrochages à l’identique permettant de mesurer la persistance des critères de l’art. La métaphore de la reprise est vivace, selon que le musée reconstitue une salle (Van Abbemuseum, Centre Pompidou) ou laisse des sosies, des copies d’œuvres coloniser sa collection permanente pour mieux révéler ses lacunes (Musée d’art moderne de la Ville de Paris). Une fois les critères d’authenticité, d’originalité, d’unicité balayés et déplacés, le répertoire de l’imitation assumée est sans doute le plus perturbant, chez les groupes d’artistes anonymes agissant comme des musées fictifs (Museum of American Art, Berlin, Salon de Fleurus, New York).New paradigms have considerably changed concepts of exhibit design in modern and contemporary art museums, favouring a self-critical and dynamic rereading by these museums of their collections, and of twentieth century art history in general. The previous widely accepted views are now being challenged. Former exhibitions are being repeated and reconstructed, and different patterns can be observed when exploring different tracks. The range of celebratory exhibitions on the occasion of centennials (the Sonderbund in Cologne, the Armory Show in New York, or Biennales in Venice) can also diverge from the stammering of history: missing documented works, exhibition halls that have been nested, or taken apart or displaced, identical hanging of works to measure the persistence of the criteria of art. The metaphor of the repeat performance, whereby the museum reconstructs a room (Van Abbemuseum, Centre Pompidou), or leaves duplicates, copies of works that have occupied its permanent collection to better reveal what is lacking (Museum of Modern Art of the City of Paris). Once the criteria of authenticity, originality, and uniqueness are put aside, the repertory of assumed imitation is undoubtedly the most disturbing, as seen in groups of anonymous artists working as fictional museums

The Ursinus Weekly, May 29, 1903

The English mystery play • Baseball • An essential force in the development of human life • Examination schedule • Society notes • Monday Night Club • Freshman and sophomore game • An evening by Ursinus Academy • Commencement • Among the colleges • Alumni noteshttps://digitalcommons.ursinus.edu/weekly/3089/thumbnail.jp

Tableaux and the Asymmetric Simple Exclusion Process

Various types of tableaux have recently been introduced due to a connection with the asymmetric simple exclusion process (ASEP) and have been the object of study in many recent papers. Relevant to this thesis, there have been several conjectures made regarding two such types of tableaux, namely staircase tableaux and tree--like tableaux. This thesis confirms these conjectures while proving other interesting results. More specifically, Hitczenko and Janson proved that distribution of symbols on the first diagonal of staircase tableaux is asymptotically normal, and they conjectured that other diagonals would be asymptotically Poisson. This thesis proves that conjecture for the kth diagonal where k is fixed. In addition, Laborde Zubieta gave a conjecture on the total number of corners in tree--like tableaux and the total number of corners in symmetric tree--like tableaux. Both conjectures are proven in this thesis. The proofs of these two conjectures are based on bijections with permutation tableaux and type--B permutation tableaux and consequently, results for these tableaux are also given. In addition, the limiting distributions of the number of occupied corners in tree--like tableaux and the number of diagonal boxes in symmetric tree--like tableaux are derived. These theorems extend results of Laborde-Zubieta and Aval et al. respectively.Ph.D., Mathematics -- Drexel University, 201

The Ursinus Weekly, May 15, 1903

Tennyson\u27s religion • Baseball • Society notes • Monday Night Club • Commencement honors • Strawberry festival • Academy entertainment • Among the colleges • Alumni receptionhttps://digitalcommons.ursinus.edu/weekly/3087/thumbnail.jp