scholarly journals Unital versions of the higher order peak algebras

2009 ◽  
Vol DMTCS Proceedings vol. AK,... (Proceedings) ◽  
Author(s):  
Marcelo Aguiar ◽  
Jean-Christophe Novelli ◽  
Jean-Yves Thibon
Keyword(s):  
Higher Order ◽  
Type B ◽  
The Third ◽  
Nous Montrons ◽  
International Audience

International audience We construct unital extensions of the higher order peak algebras defined by Krob and the third author in [Ann. Comb. 9 (2005), 411―430], and show that they can be obtained as homomorphic images of certain subalgebras of the Mantaci-Reutenauer algebras of type $B$. This generalizes a result of Bergeron, Nyman and the first author [Trans. AMS 356 (2004), 2781―2824]. Nous construisons des extensions unitaires des algèbres de pics d'ordre supérieur définies par Krob et le troisième auteur dans [Ann. Comb. 9 (2005), 411―430], et nous montrons qu'elles peuvent être obtenues comme images homomorphes de certaines sous-algèbres des algèbres de Mantaci-Reutenauer de type $B$. Ceci généralise un résultat dû à Bergeron, Nyman et au premier auteur [Trans. AMS 356 (2004), 2781―2824].

scholarly journals Mixed volumes of hypersimplices

2015 ◽  
Vol DMTCS Proceedings, 27th... (Proceedings) ◽  
Author(s):  
Gaku Liu
Keyword(s):  
Catalan Numbers ◽  
Binomial Coefficients ◽  
Type B ◽  
Combinatorial Interpretation ◽  
Mixed Volumes ◽  
Eulerian Numbers ◽  
Eulerian Number ◽  
Nous Montrons ◽  
Set Of Permutations ◽  
International Audience

International audience In this extended abstract we consider mixed volumes of combinations of hypersimplices. These numbers, called mixed Eulerian numbers, were first considered by A. Postnikov and were shown to satisfy many properties related to Eulerian numbers, Catalan numbers, binomial coefficients, etc. We give a general combinatorial interpretation for mixed Eulerian numbers and prove the above properties combinatorially. In particular, we show that each mixed Eulerian number enumerates a certain set of permutations in $S_n$. We also prove several new properties of mixed Eulerian numbers using our methods. Finally, we consider a type $B$ analogue of mixed Eulerian numbers and give an analogous combinatorial interpretation for these numbers. Dans ce résumé étendu nous considérons les volumes mixtes de combinaisons d’hyper-simplexes. Ces nombres, appelés les nombres Eulériens mixtes, ont été pour la première fois étudiés par A. Postnikov, et il a été montré qu’ils satisfont à de nombreuses propriétés reliées aux nombres Eulériens, au nombres de Catalan, aux coefficients binomiaux, etc. Nous donnons une interprétation combinatoire générale des nombres Eulériens mixtes, et nous prouvons combinatoirement les propriétés mentionnées ci-dessus. En particulier, nous montrons que chaque nombre Eulérien mixte compte les éléments d’un certain sous-ensemble de l’ensemble des permutations $S_n$. Nous établissons également plusieurs nouvelles propriétés des nombres Eulériens mixtes grâce à notre méthode. Pour finir, nous introduisons une généralisation en type $B$ des nombres Eulériens mixtes, et nous en donnons une interprétation combinatoire analogue.

scholarly journals Crossings and nestings in set partitions of classical types

2010 ◽  
Vol DMTCS Proceedings vol. AN,... (Proceedings) ◽  
Author(s):  
Martin Rubey ◽  
Christian Stump
Keyword(s):  
Nous Avons ◽  
Type A ◽  
The Other ◽  
Type B ◽  
Set Partition ◽  
Set Partitions ◽  
Type D ◽  
Nous Montrons ◽  
International Audience ◽  
The One

International audience In this extended abstract, we investigate bijections on various classes of set partitions of classical types that preserve openers and closers. On the one hand we present bijections for types $B$ and $C$ that interchange crossings and nestings, which generalize a construction by Kasraoui and Zeng for type $A$. On the other hand we generalize a bijection to type $B$ and $C$ that interchanges the cardinality of a maximal crossing with the cardinality of a maximal nesting, as given by Chen, Deng, Du, Stanley and Yan for type $A$. For type $D$, we were only able to construct a bijection between non-crossing and non-nesting set partitions. For all classical types we show that the set of openers and the set of closers determine a non-crossing or non-nesting set partition essentially uniquely. Dans ce résumé, nous étudions des bijections entre diverses classes de partitions d'ensemble de types classiques qui préservent les "openers'' et les "closers''. D'une part, nous présentons des bijections pour les types $B$ et $C$ qui échangent croisées et emboôtées, qui généralisent une construction de Kasraoui et Zeng pour le type $A$. D'autre part, nous généralisons une bijection pour le type $B$ et $C$ qui échange la cardinalité d'un croisement maximal avec la cardinalité d'un emboîtement maximal comme il a été fait par Chen, Deng, Du, Stanley et Yan pour le type $A$. Pour le type $D$, nous avons seulement construit une bijection entre les partitions non croisées et non emboîtées. Pour tout les types classiques, nous montrons que l'ensemble des "openers'' et l'ensemble des "closers'' déterminent une partition non croisées ou non emboîtées essentiellement de façon unique.

Somethin’ about Scandinavia: Danish Shorts on the Post-war International Scene

2018 ◽  
Author(s):  
C. Claire Thomson
Keyword(s):  
United Nations ◽  
International Collaboration ◽  
Marshall Plan ◽  
The Third ◽  
Animated Film ◽  
International Audience ◽  
Post War ◽  
Nordic Cooperation

Building on the picture of post-war Anglo-Danish documentary collaboration established in the previous chapter, this chapter examines three cases of international collaboration in which Dansk Kulturfilm and Ministeriernes Filmudvalg were involved in the late 1940s and 1950s. They Guide You Across (Ingolf Boisen, 1949) was commissioned to showcase Scandinavian cooperation in the realm of aviation (SAS) and was adopted by the newly-established United Nations Film Board. The complexities of this film’s production, funding and distribution are illustrative of the activities of the UN Film Board in its first years of operation. The second case study considers Alle mine Skibe (All My Ships, Theodor Christensen, 1951) as an example of a film commissioned and funded under the auspices of the Marshall Plan. This US initiative sponsored informational films across Europe, emphasising national solutions to post-war reconstruction. The third case study, Bent Barfod’s animated film Noget om Norden (Somethin’ about Scandinavia, 1956) explains Nordic cooperation for an international audience, but ironically exposed some gaps in inter-Nordic collaboration in the realm of film.

Gescheiden en dan ? :Herpartneren in Vlaanderen anno 2010

2013 ◽  
Vol 3 (3) ◽  
pp. 1-66
Author(s):  
Inge Pasteels ◽  
Dimitri Mortelmans
Keyword(s):  
Higher Order ◽  
Gender Perspective ◽  
Partner Status ◽  
The Third ◽  
Current Partner ◽  
Different Types ◽  
Unmarried Cohabitation ◽  
Mate Waarin

In deze bijdrage wordt het herpartneren na een scheiding uit een eerste huwelijk beschreven. Met gegevens van “Scheiding in Vlaanderen” verzameld bij 1192 mannen en 1448 vrouwen gescheiden tussen 1981 en 2005, wordt vooreerst de timing van het herpartneren alsook de leefvorm waarvoor men kiest in postmaritale relaties, bestudeerd. We onderscheiden LAT‐relaties, ongehuwd samenwoonrelaties en tweede huwelijken. Daarna wordt de huidige partnerstatus van gescheidenen anno 2010 in kaart gebracht. Ten derde komt de mate waarin partners uit eerste huwelijken of postmaritale relaties gelijkend zijn aan bod. Vervolgens wordt de stabiliteit van LAT‐relaties of ongehuwde samenwoonrelaties na een eerste huwelijk bestudeerd. Een beschrijving van postmaritale relatietrajecten met aandacht voor relatierang en relatietype rondt deze bijdrage af. Alle analyses worden apart uitgevoerd voor mannen en vrouwen van verschillende scheidingscohorten. Abstract : Using surveydata of “Divorce in Flanders” for 1192 men and 1448 women, divorced between 1981 and 2005, we explore repartnering after a first divorce. Firstly, prevalence and timing of repartnering are examined. LAT‐relationships, unmarried cohabitation and remarriage are considered as different types of repartnering. Secondly, the current partner status for divorcees in 2010 is described. Homogamy in first marriages and in higher order relationships is the third topic in this article. At last, stability of postmarital relationships and partnership trajectories are explored. Data are analyzed using a cohort perspective and a gender perspective.

scholarly journals Macdonald polynomials at $t=q^k$

2009 ◽  
Vol DMTCS Proceedings vol. AK,... (Proceedings) ◽  
Author(s):  
Jean-Gabriel Luque
Keyword(s):  
Macdonald Polynomials ◽  
Nous Montrons ◽  
International Audience

International audience We investigate the homogeneous symmetric Macdonald polynomials $P_{\lambda} (\mathbb{X} ;q,t)$ for the specialization $t=q^k$. We show an identity relying the polynomials $P_{\lambda} (\mathbb{X} ;q,q^k)$ and $P_{\lambda} (\frac{1-q}{1-q^k}\mathbb{X} ;q,q^k)$. As a consequence, we describe an operator whose eigenvalues characterize the polynomials $P_{\lambda} (\mathbb{X} ;q,q^k)$. Nous nous intéressons aux propriétés des polynômes de Macdonald symétriques $P_{\lambda} (\mathbb{X} ;q,t)$ pour la spécialisation $t=q^k$. En particulier nous montrons une égalité reliant les polynômes $P_{\lambda} (\mathbb{X} ;q,q^k)$ et $P_{\lambda} (\frac{1-q}{1-q^k}\mathbb{X} ;q,q^k)$. Nous en déduisons la description d'un opérateur dont les valeurs propres caractérisent les polynômes $P_{\lambda} (\mathbb{X} ;q,q^k)$.

scholarly journals Troisi\`eme groupe de cohomologie non ramifi\'ee d'un solide cubique sur un corps de fonctions d'une variable

2018 ◽  
Vol Volume 2 ◽  
Author(s):  
Jean-Louis Colliot-Thélène ◽  
Alena Pirutka
Keyword(s):  
Function Field ◽  
Cohomology Group ◽  
Chow Group ◽  
Hodge Conjecture ◽  
Complex Curve ◽  
The Third ◽  
Generic Fibre ◽  
Nous Montrons ◽  
Unramified Cohomology ◽  
Cubic Threefold

En combinant une m\'ethode de C. Voisin avec la descente galoisienne sur le groupe de Chow en codimension $2$, nous montrons que le troisi\`eme groupe de cohomologie non ramifi\'ee d'un solide cubique lisse d\'efini sur le corps des fonctions d'une courbe complexe est nul. Ceci implique que la conjecture de Hodge enti\`ere pour les classes de degr\'e 4 vaut pour les vari\'et\'es projectives et lisses de dimension 4 fibr\'ees en solides cubiques au-dessus d'une courbe, sans restriction sur les fibres singuli\`eres. --------------- We prove that the third unramified cohomology group of a smooth cubic threefold over the function field of a complex curve vanishes. For this, we combine a method of C. Voisin with Galois descent on the codimension $2$ Chow group. As a corollary, we show that the integral Hodge conjecture holds for degree $4$ classes on smooth projective fourfolds equipped with a fibration over a curve, the generic fibre of which is a smooth cubic threefold, with arbitrary singularities on the special fibres. Comment: in French

scholarly journals Cataland: Why the Fuss?

2020 ◽  
Vol DMTCS Proceedings, 28th... ◽  
Author(s):  
Christian Stump ◽  
Hugh Thomas ◽  
Nathan Williams
Keyword(s):  
Coxeter System ◽  
Cluster Complexes ◽  
The Third ◽  
International Audience

International audience The main objects of noncrossing Catalan combinatorics associated to a finite Coxeter system are noncross- ing partitions, sortable elements, and cluster complexes. The first and the third of these have known Fuss–Catalan generalizations. We provide new viewpoints for these, introduce a corresponding generalization of sortable elements as elements in the positive Artin monoid, and show how this perspective ties together all three generalizations.

A SPECTRAL/hp NONLINEAR FINITE ELEMENT ANALYSIS OF HIGHER-ORDER BEAM THEORY WITH VISCOELASTICITY

2012 ◽  
Vol 04 (01) ◽  
pp. 1250010 ◽  
Author(s):  
V. P. VALLALA ◽  
G. S. PAYETTE ◽  
J. N. REDDY
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Virtual Work ◽  
Constitutive Relations ◽  
Beam Theory ◽  
Element Model ◽  
Higher Order ◽  
Time Step ◽  
Third Order ◽  
The Third

In this paper, a finite element model for efficient nonlinear analysis of the mechanical response of viscoelastic beams is presented. The principle of virtual work is utilized in conjunction with the third-order beam theory to develop displacement-based, weak-form Galerkin finite element model for both quasi-static and fully-transient analysis. The displacement field is assumed such that the third-order beam theory admits C0 Lagrange interpolation of all dependent variables and the constitutive equation can be that of an isotropic material. Also, higher-order interpolation functions of spectral/hp type are employed to efficiently eliminate numerical locking. The mechanical properties are considered to be linear viscoelastic while the beam may undergo von Kármán nonlinear geometric deformations. The constitutive equations are modeled using Prony exponential series with general n-parameter Kelvin chain as its mechanical analogy for quasi-static cases and a simple two-element Maxwell model for dynamic cases. The fully discretized finite element equations are obtained by approximating the convolution integrals from the viscous part of the constitutive relations using a trapezoidal rule. A two-point recurrence scheme is developed that uses the approximation of relaxation moduli with Prony series. This necessitates the data storage for only the last time step and not for the entire deformation history.

scholarly journals MATRIX MODEL PERTURBED BY HIGHER ORDER CURVATURE TERMS

1992 ◽  
Vol 07 (33) ◽  
pp. 3081-3100 ◽  
Author(s):  
G.P. KORCHEMSKY
Keyword(s):  
Phase Diagram ◽  
Matrix Model ◽  
Critical Behavior ◽  
Intermediate Phase ◽  
Higher Order ◽  
Bosonic String ◽  
Branched Polymers ◽  
Nonlocal Term ◽  
Random Surfaces ◽  
The Third

The critical behavior of the D=0 matrix model with the potential perturbed by a nonlocal term generating touchings between random surfaces is studied. It is found that the phase diagram of the model has many features of the phase diagram of discretized Polyakov’s bosonic string with higher order curvature terms included. It contains the phase of smooth (Liouville) surfaces, the intermediate phase and the phase of branched polymers. The perturbation becomes irrelevant at the first phase and dominates at the third one.

Sign in / Sign up

Export Citation Format

Share Document