scholarly journals The Sperner property for 132‐avoiding intervals in the weak order

2020 ◽  
Author(s):  
Christian Gaetz ◽  
Katherine Tung
Keyword(s):  
Weak Order ◽  
Sperner Property

scholarly journals Order compatibility for Cauchy spaces and convergence spaces

1987 ◽  
Vol 10 (2) ◽  
pp. 209-216
Author(s):  
D. C. Kent ◽  
Reino Vainio
Keyword(s):  
Uniform Convergence ◽  
Weak Order ◽  
Convergence Spaces ◽  
Convergence Structure ◽  
Cauchy Structure ◽  
Cauchy Spaces

A Cauchy structure and a preorder on the same set are said to be compatible if both arise from the same quasi-uniform convergence structure onX. Howover, there are two natural ways to derive the former structures from the latter, leading to “strong” and “weak” notions of order compatibility for Cauchy spaces. These in turn lead to characterizations of strong and weak order compatibility for convergence spaces.

scholarly journals On the Topology of the Cambrian Semilattices

10.37236/2910 ◽  
2013 ◽  
Vol 20 (2) ◽  
Author(s):  
Myrto Kallipoliti ◽  
Henri Mühle
Keyword(s):  
Coxeter Group ◽  
Closed Interval ◽  
Open Interval ◽  
Weak Order ◽  
Edge Labeling

For an arbitrary Coxeter group $W$, Reading and Speyer defined Cambrian semilattices $\mathcal{C}_{\gamma}$ as sub-semilattices of the weak order on $W$ induced by so-called $\gamma$-sortable elements. In this article, we define an edge-labeling of $\mathcal{C}_{\gamma}$, and show that this is an EL-labeling for every closed interval of $\mathcal{C}_{\gamma}$. In addition, we use our labeling to show that every finite open interval in a Cambrian semilattice is either contractible or spherical, and we characterize the spherical intervals, generalizing a result by Reading.

scholarly journals How to get the weak order out of a digraph ?

2015 ◽  
Vol DMTCS Proceedings, 27th... (Proceedings) ◽  
Author(s):  
Francois Viard
Keyword(s):  
Wreath Product ◽  
Symmetric Function ◽  
Coxeter Groups ◽  
Symmetric Functions ◽  
Weak Order ◽  
Möbius Function ◽  
Mobius Function ◽  
Acyclic Digraph ◽  
International Audience

International audience We construct a poset from a simple acyclic digraph together with a valuation on its vertices, and we compute the values of its Möbius function. We show that the weak order on Coxeter groups $A$<sub>$n-1$</sub>, $B$<sub>$n$</sub>, $Ã$<sub>$n$</sub>, and the flag weak order on the wreath product &#8484;<sub>$r$</sub> &#8768; $S$<sub>$n$</sub> introduced by Adin, Brenti and Roichman (2012), are special instances of our construction. We conclude by briefly explaining how to use our work to define quasi-symmetric functions, with a special emphasis on the $A$<sub>$n-1$</sub> case, in which case we obtain the classical Stanley symmetric function. On construit une famille d’ensembles ordonnés à partir d’un graphe orienté, simple et acyclique munit d’une valuation sur ses sommets, puis on calcule les valeurs de leur fonction de Möbius respective. On montre que l’ordre faible sur les groupes de Coxeter $A$<sub>$n-1$</sub>, $B$<sub>$n$</sub>, $Ã$<sub>$n$</sub>, ainsi qu’une variante de l’ordre faible sur les produits en couronne &#8484;<sub>$r$</sub> &#8768; $S$<sub>$n$</sub> introduit par Adin, Brenti et Roichman (2012), sont des cas particuliers de cette construction. On conclura en expliquant brièvement comment ce travail peut-être utilisé pour définir des fonction quasi-symétriques, en insistant sur l’exemple de l’ordre faible sur $A$<sub>$n-1$</sub> où l’on obtient les séries de Stanley classiques.

scholarly journals Weak Markov operators

Filomat ◽  
2018 ◽  
Vol 32 (15) ◽  
pp. 5453-5457
Author(s):  
Hūlya Duru ◽  
Serkan Ilter
Keyword(s):  
Positive Operator ◽  
Extreme Points ◽  
Markov Operator ◽  
Weak Order ◽  
Markov Operators

Let A and B be f -algebras with unit elements eA and eB respectively. A positive operator T from A to B satisfying T(eA) = eB is called a Markov operator. In this definition we replace unit elements with weak order units and, in this case, call T to be a weak Markov operator. In this paper, we characterize extreme points of the weak Markov operators.

scholarly journals On the Weak Order Ideal Associated to Linear Codes

2018 ◽  
Vol 12 (3) ◽  
pp. 339-347 ◽  
Author(s):  
Mijail Borges-Quintana ◽  
Miguel Ángel Borges-Trenard ◽  
Edgar Martínez-Moro
Keyword(s):  
Linear Codes ◽  
Weak Order ◽  
Order Ideal
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