scholarly journals Universal geometric coefficients for the four-punctured sphere (Extended Abstract)

2015 ◽  
Vol DMTCS Proceedings, 27th... (Proceedings) ◽  
Author(s):  
Emily Barnard ◽  
Emily Meehan ◽  
Shira Polster ◽  
Nathan Reading
Keyword(s):  
Cluster Algebra ◽  
Short List ◽  
Nous Permet ◽  
Rational Part ◽  
International Audience

International audience We construct universal geometric coefficients for the cluster algebra associated to the four-punctured sphere and obtain, as a by-product, the $g$ -vectors of cluster variables. We also construct the rational part of the mutation fan. These constructions rely on a classification of the allowable curves (the curves which can appear in quasi-laminations). The classification allows us to prove the Null Tangle Property for the four-punctured sphere, thus adding this surface to a short list of surfaces for which this property is known. The Null Tangle Property then implies that the shear coordinates of allowable curves are the universal coefficients. We compute these shear coordinates to obtain universal geometric coefficients. Nous construisons des coefficients géométriques universels pour l’algèbre amassée associée à la sphère privée de 4 points, et obtenons ce faisant les $g$-vecteurs des variables d’amas. Nous construisons aussi la partie rationnelle de l’éventail de mutation. Ces constructions reposent sur la classification des courbes admissibles (les courbes qui peuvent apparaître dans les quasi-laminations). Cette classification nous permet de prouver la “Null Tangle Property” pour la sphère privée de 4 points, ajoutant ainsi cette surface à la courte liste de surfaces pour lesquelles cette propriété est connue. La “Null Tangle Property” implique alors que les coordonnées de décalage des courbes admissibles sont les coefficients universels. Nous calculons ces coordonnées de décalage pour obtenir les coefficients géométriques universels.

scholarly journals Finite Eulerian posets which are binomial or Sheffer

2011 ◽  
Vol DMTCS Proceedings vol. AO,... (Proceedings) ◽  
Author(s):  
Hoda Bidkhori
Keyword(s):  
Generating Functions ◽  
Complete Classification ◽  
International Audience ◽  
Original Question ◽  
Eulerian Posets

International audience In this paper we study finite Eulerian posets which are binomial or Sheffer. These important classes of posets are related to the theory of generating functions and to geometry. The results of this paper are organized as follows: (1) We completely determine the structure of Eulerian binomial posets and, as a conclusion, we are able to classify factorial functions of Eulerian binomial posets; (2) We give an almost complete classification of factorial functions of Eulerian Sheffer posets by dividing the original question into several cases; (3) In most cases above, we completely determine the structure of Eulerian Sheffer posets, a result stronger than just classifying factorial functions of these Eulerian Sheffer posets. We also study Eulerian triangular posets. This paper answers questions posed by R. Ehrenborg and M. Readdy. This research is also motivated by the work of R. Stanley about recognizing the \emphboolean lattice by looking at smaller intervals. Nous étudions les ensembles partiellement ordonnés finis (EPO) qui sont soit binomiaux soit de type Sheffer (deux notions reliées aux séries génératrices et à la géométrie). Nos résultats sont les suivants: (1) nous déterminons la structure des EPO Euleriens et binomiaux; nous classifions ainsi les fonctions factorielles de tous ces EPO; (2) nous donnons une classification presque complète des fonctions factorielles des EPO Euleriens de type Sheffer; (3) dans la plupart de ces cas, nous déterminons complètement la structure des EPO Euleriens et Sheffer, ce qui est plus fort que classifier leurs fonctions factorielles. Nous étudions aussi les EPO Euleriens triangulaires. Cet article répond à des questions de R. Ehrenborg and M. Readdy. Il est aussi motivé par le travail de R. Stanley sur la reconnaissance du treillis booléen via l'étude des petits intervalles.

scholarly journals $Y$ -meshes and generalized pentagram maps

2015 ◽  
Vol DMTCS Proceedings, 27th... (Proceedings) ◽  
Author(s):  
Max Glick ◽  
Pavlo Pylyavskyy
Keyword(s):  
Projective Geometry ◽  
Cluster Algebra ◽  
Cluster Theory ◽  
Rich Family ◽  
International Audience ◽  
Pentagram Map

International audience We introduce a rich family of generalizations of the pentagram map sharing the property that each generates an infinite configuration of points and lines with four points on each line. These systems all have a description as $Y$ -mutations in a cluster algebra and hence establish new connections between cluster theory and projective geometry. Nous introduisons une famille de généralisations de l’application pentagramme. Chacune produit une configuration infinie de points et de lignes avec quatre points sur chaque ligne. Ces systèmes ont une description des $Y$ -mutations dans une algèbre amassée, un nouveau lien entre la théorie d’algèbres amassées et la géométrie projective.

‘They had added not a single tiny proposition’: The Reception of the Prior Analytics in the First Half of the Twelfth Century

Vivarium ◽  
2010 ◽  
Vol 48 (1-2) ◽  
pp. 159-192 ◽  
Author(s):  
Christopher J. Martin
Keyword(s):  
Twelfth Century ◽  
Short List ◽  
General Terms ◽  
Formal Validity

AbstractA study of the reception of Aristotle’s Prior Analytics in the first half of the twelfth century. It is shown that Peter Abaelard was perhaps acquainted with as much as the first seven chapters of Book I of the Prior Analytics but with no more. The appearance at the beginning of the twelfth century of a short list of dialectical loci which has puzzled earlier commentators is explained by noting that this list formalises the classification of extensional relations between general terms and that this classification had already be put forward by Boethius in his de Syllogismo Categorico and Introductio ad Syllogismos Categoricas. It is pointed out the kind of text referred to as an ‘Introductio’ at the beginning of the twelfth-century follows very closely the structure of Boethius own Introductio and adds to it material drawn from his accounts of loci and the conditional propositions. It is argued that the reception of the Prior Analytics has to be understood against the background of this well developed tradition of treating together syllogisms, loci, and conditional propostions. Referring to a challenge to the formal validity of Darapti in the Ars Meliduna the paper concludes by illustrating that the theory of the syllogism presented in Prior Analytics was still controversial in the middle of the twelfth-century.

Bone Dysplasias

2018 ◽  
Author(s):  
Jürgen W. Spranger ◽  
Paula W. Brill ◽  
Christine Hall ◽  
Gen Nishimura ◽  
Andrea Superti-Furga ◽  
...  
Keyword(s):  
Bone Density ◽  
Clinical Features ◽  
Differential Diagnoses ◽  
Short List ◽  
Age Related ◽  
Bone Dysplasias ◽  
Text Presentation ◽  
Skeletal Disorders

This is a unique atlas presenting age-related radiographs on more than 250 rare constitutional skeletal diseases (dysplasias, dysostoses, osteolyses, disorders of bone density, and more) focusing on diagnostically essential radiographic and clinical features. Each chapter is supplemented with prognostic and therapeutic information, a guide to differential diagnoses, and a short list of the most relevant publications. A major advantage is the systematic conformation of chapters, sparing the reader a cumbersome read-through of longer text. Presentation in accordance with the most recent International Nosology and Classification of Genetic Skeletal Disorders.

scholarly journals Geometric classification of simple graph algebras

2012 ◽  
Vol 33 (4) ◽  
pp. 1199-1220 ◽  
Author(s):  
ADAM P. W. SØRENSEN
Keyword(s):  
Finite Type ◽  
Isomorphism Class ◽  
Simple Graph ◽  
The Other ◽  
Graph Algebras ◽  
Short List

AbstractInspired by Franks’ classification of irreducible shifts of finite type, we provide a short list of allowed moves on graphs that preserve the stable isomorphism class of the associated $C^*$-algebras. We show that if two graphs have stably isomorphic and simple unital algebras then we can use these moves to transform one into the other.

scholarly journals Equivalences for pattern avoiding involutions and classification

2008 ◽  
Vol DMTCS Proceedings vol. AJ,... (Proceedings) ◽  
Author(s):  
Mark Dukes ◽  
Vít Jelínek ◽  
Toufik Mansour ◽  
Astrid Reifegerste
Keyword(s):  
Symmetric Group ◽  
Signed Permutations ◽  
International Audience

International audience We complete the Wilf classification of signed patterns of length 5 for both signed permutations and signed involutions. New general equivalences of patterns are given which prove Jaggard's conjectures concerning involutions in the symmetric group avoiding certain patterns of length 5 and 6. In this way, we also complete the Wilf classification of $S_5$, $S_6$, and $S_7$ for both permutations and involutions. Nous complétons la classification de Wilf des motifs signés de longueur 5 à la fois pour les permutations signées et les involutions signées. Nous donnons de nouvelles équivalences générales de motifs qui prouvent les conjectures de Jaggard concernant les involutions dans le groupe symétrique évitant certains motifs de longueur 5 et 6. De cette manière nous complétons également la classification de Wilf de $S_5$, $S_6$ et $S_7$ à la fois pour les permutations et les involutions.

scholarly journals Classification of skew translation generalized quadrangles, I

2015 ◽  
Vol Vol. 17 no. 1 (Combinatorics) ◽  
Author(s):  
Koen Thas
Keyword(s):  
Generalized Quadrangles ◽  
New Classification ◽  
Open Problems ◽  
International Audience ◽  
Rank 2

Combinatorics International audience We describe new classification results in the theory of generalized quadrangles (= Tits-buildings of rank 2 and type B2), more precisely in the (large) subtheory of skew translation generalized quadrangles (``STGQs''). Some of these involve, and solve, long-standing open problems.

scholarly journals TraduXio Project: Latest Upgrades and Feedback

2021 ◽  
Vol Atelier Digit_Hum (Digital humanities in...) ◽  
Author(s):  
Philippe Lacour ◽  
Aurélien Bénel
Keyword(s):  
Language Learning ◽  
Computer Assisted ◽  
Digital Environment ◽  
Professional Skill ◽  
Web Based ◽  
Privilege Management ◽  
Recent Developments ◽  
History Of ◽  
International Audience

International audience TraduXio is a digital environment for computer assisted multilingual translation which is web-based, free to use and with an open source code. Its originality is threefold-whereas traditional technologies are limited to two languages (source/target), TraduXio enables the comparison of different versions of the same text in various languages; its concordancer provides relevant and multilingual suggestions through a classification of the source according to the history, genre and author; it uses collaborative devices (privilege management, forums, networks, history of modification, etc.) to promote collective (and distributed) translation. TraduXio is designed to encourage the diversification of language learning and to promote a reappraisal of translation as a professional skill. It can be used in many different ways, by very diverse kind of people. In this presentation, I will present the recent developments of the software (its version 2.1) and illustrate how specific groups (language teaching, social sciences, literature) use it on a regular basis. In this paper, I present the technology but concentrate more on the possible uses of TraduXio, thus focusing on translators' feedback about their experience when working in this digital environment in a truly collaborative way.

scholarly journals The cluster and dual canonical bases of Z [x_11, ..., x_33] are equal

2010 ◽  
Vol DMTCS Proceedings vol. AN,... (Proceedings) ◽  
Author(s):  
Brendon Rhoades
Keyword(s):  
Quantum Group ◽  
Polynomial Ring ◽  
Geometric Model ◽  
Cluster Algebra ◽  
Canonical Basis ◽  
The Other ◽  
Monomial Basis ◽  
Dual Canonical Basis ◽  
Nous Montrons ◽  
International Audience

International audience The polynomial ring $\mathbb{Z}[x_{11}, . . . , x_{33}]$ has a basis called the dual canonical basis whose quantization facilitates the study of representations of the quantum group $U_q(\mathfrak{sl}3(\mathbb{C}))$. On the other hand, $\mathbb{Z}[x_{11}, . . . , x_{33}]$ inherits a basis from the cluster monomial basis of a geometric model of the type $D_4$ cluster algebra. We prove that these two bases are equal. This extends work of Skandera and proves a conjecture of Fomin and Zelevinsky. This also provides an explicit factorization of the dual canonical basis elements of $\mathbb{Z}[x_{11}, . . . , x_{33}]$ into irreducible polynomials. L'anneau de polynômes $\mathbb{Z}[x_{11}, . . . , x_{33}]$ a une base appelée base duale canonique, et dont une quantification facilite l'étude des représentations du groupe quantique $U_q(\mathfrak{sl}3(\mathbb{C}))$. D'autre part, $\mathbb{Z}[x_{11}, . . . , x_{33}]$ admet une base issue de la base des monômes d'amas de l'algèbre amassée géométrique de type $D_4$. Nous montrons que ces deux bases sont égales. Ceci prolonge les travaux de Skandera et démontre une conjecture de Fomin et Zelevinsky. Ceci fournit également une factorisation explicite en polynômes irréductibles des éléments de la base duale canonique de $\mathbb{Z}[x_{11}, . . . , x_{33}]$ .

scholarly journals Connectedness of number theoretical tilings

2005 ◽  
Vol Vol. 7 ◽  
Author(s):  
Shigeki Akiyama ◽  
Nertila Gjini
Keyword(s):  
Complete Classification ◽  
Necessary And Sufficient Condition ◽  
Digit Set ◽  
Number Systems ◽  
Arcwise Connected ◽  
International Audience ◽  
Consecutive Integers ◽  
Pisot Unit ◽  
Necessary And Sufficient

International audience Let T=T(A,D) be a self-affine tile in \reals^n defined by an integral expanding matrix A and a digit set D. In connection with canonical number systems, we study connectedness of T when D corresponds to the set of consecutive integers \0,1,..., |det(A)|-1\. It is shown that in \reals^3 and \reals^4, for any integral expanding matrix A, T(A,D) is connected. We also study the connectedness of Pisot dual tilings which play an important role in the study of β -expansion, substitution and symbolic dynamical system. It is shown that each tile generated by a Pisot unit of degree 3 is arcwise connected. This is naturally expected since the digit set consists of consecutive integers as above. However surprisingly, we found families of disconnected Pisot dual tiles of degree 4. Also we give a simple necessary and sufficient condition for the connectedness of the Pisot dual tiles of degree 4. As a byproduct, a complete classification of the β -expansion of 1 for quartic Pisot units is given.

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