scholarly journals Classification of large Pólya-Eggenberger urns with regard to their asymptotics

2005 ◽  
Vol DMTCS Proceedings vol. AD,... (Proceedings) ◽  
Author(s):  
Nicolas Pouyanne
Keyword(s):  
Algebraic Approach ◽  
Urn Models ◽  
Search Trees ◽  
International Audience

International audience This article deals with Pólya generalized urn models with constant balance in any dimension. It is based on the algebraic approach of Pouyanne (2005) and classifies urns having "large'' eigenvalues in five classes, depending on their almost sure asymptotics. These classes are described in terms of the spectrum of the urn's replacement matrix and examples of each case are treated. We study the cases of so-called cyclic urns in any dimension and $m$-ary search trees for $m \geq 27$.

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 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.

HAAG DUALITY IN CONFORMAL QUANTUM FIELD THEORY

1990 ◽  
Vol 02 (01) ◽  
pp. 105-125 ◽  
Author(s):  
DETLEV BUCHHOLZ ◽  
HANNS SCHULZ-MIRBACH
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Central Charge ◽  
Algebraic Approach ◽  
Energy Tensor ◽  
Quantum Field ◽  
Haag Duality ◽  
Conformal Fields ◽  
Stress Energy

Haag duality is established in conformal quantum field theory for observable fields on the compactified light ray S1 and Minkowski space S1×S1, respectively. This result provides the foundation for an algebraic approach to the classification of conformal theories. Haag duality can fail, however, for the restriction of conformal fields to the underlying non-compact spaces ℝ, respectively ℝ×ℝ. A prominent example is the stress energy tensor with central charge c>1.

AN ALGEBRAIC THEORY FOR REGULAR LANGUAGES OF FINITE AND INFINITE WORDS

1993 ◽  
Vol 03 (04) ◽  
pp. 447-489 ◽  
Author(s):  
THOMAS WILKE
Keyword(s):  
Algebraic Theory ◽  
Algebraic Approach ◽  
Regular Languages ◽  
Cantor Space ◽  
Infinite Words ◽  
Finite Semigroups ◽  
Borel Hierarchy ◽  
Algebraic Description ◽  
One To One

An algebraic approach to the theory of regular languages of finite and infinite words (∞-languages) is presented. It extends the algebraic theory of regular languages of finite words, which is based on finite semigroups. Their role is taken over by a structure called right binoid. A variety theorem is proved: there is a one-to-one correspondence between varieties of ∞-languages and pseudovarieties of right binoids. The class of locally threshold testable languages and several natural subclasses (such as the class of locally testable languages) as well as classes of the Borel hierarchy over the Cantor space (restricted to regular languages) are investigated as examples for varieties of ∞-languages. The corresponding pseudovarieties of right binoids are characterized and in some cases defining equations are derived. The connections with the algebraic description and classification of regular languages of infinite words in terms of finite semigroups are pointed out.

scholarly journals Digital search trees with m trees: Level polynomials and insertion costs

2011 ◽  
Vol Vol. 13 no. 3 (Analysis of Algorithms) ◽  
Author(s):  
Helmut Prodinger
Keyword(s):  
Analysis Of Algorithms ◽  
Approximate Counting ◽  
Search Trees ◽  
Digital Search Trees ◽  
International Audience ◽  
Digital Search

Analysis of Algorithms International audience We adapt a novel idea of Cichon's related to Approximate Counting to the present instance of Digital Search Trees, by using m (instead of one) such trees. We investigate the level polynomials, which have as coefficients the expected numbers of data on a given level, and the insertion costs. The level polynomials can be precisely described, thanks to formulae from q-analysis. The asymptotics of expectation and variance of the insertion cost are fairly standard these days and done with Rice's method.

scholarly journals Numerical Studies of the Asymptotic Height Distribution in Binary Search Trees

2003 ◽  
Vol Vol. 6 no. 1 ◽  
Author(s):  
Charles Knessl
Keyword(s):  
Integral Equation ◽  
Binary Search ◽  
Linear Integral Equation ◽  
Height Distribution ◽  
Binary Search Trees ◽  
Search Trees ◽  
Asymptotic Results ◽  
Numerical Studies ◽  
International Audience ◽  
Linear Integral

International audience We study numerically a non-linear integral equation that arises in the study of binary search trees. If the tree is constructed from n elements, this integral equation describes the asymptotic (as n→∞) distribution of the height of the tree. This supplements some asymptotic results we recently obtained for the tails of the distribution. The asymptotic height distribution is shown to be unimodal with highly asymmetric tails.

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 Group Classification Invariant Solutions of Burgers' Equation

2021 ◽  
pp. 19-32
Author(s):  
Mohammed Adam Abdualah Khatir ◽  
Mohammed Ali Basher ◽  
Blegiss Abdulaziz Abdulrahman Ebyed
Keyword(s):  
Mathematical Method ◽  
Wide Class ◽  
Burgers Equation ◽  
Algebraic Approach ◽  
Group Classification ◽  
Invariant Solutions ◽  
Smooth Functions ◽  
Preliminary Group

The aims of the present paper is to solve the problem of the group classification of the general Burgers’ equation u_t=f(x,u) u_x^2+g(x,u)u_xx, where f and g are arbitrary smooth functions of the variables x and u, by using Lie method. The paper is one of the few applications of an algebraic approach to the problem of group classification: We followed the analysis mathematical method using the method of preliminary group classification. A number of new interesting nonlinear invariant models which have nontrivial invariance algebras are obtained. The result of the work is a wide class of equations summarized in table form.

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