Theorems on strong constructibility with a compass alone

1987 ◽  
Vol 30 (1) ◽  
pp. 28-35 ◽  
Author(s):  
Arnon Avron
Keyword(s):  
Strong Constructibility

On strict strong constructibility with a compass alone

1990 ◽  
Vol 38 (1-2) ◽  
pp. 12-15 ◽  
Author(s):  
Arnon Avron
Keyword(s):  
Strong Constructibility

scholarly journals The absolute order on the hyperoctahedral group

2009 ◽  
Vol DMTCS Proceedings vol. AK,... (Proceedings) ◽  
Author(s):  
Myrto Kallipoliti
Keyword(s):  
Closed Interval ◽  
Order Ideal ◽  
Order Complex ◽  
Hyperoctahedral Group ◽  
Closed Intervals ◽  
Absolute Order ◽  
Nous Montrons ◽  
International Audience ◽  
Strong Constructibility ◽  
The Absolute

International audience The absolute order on the hyperoctahedral group $B_n$ is investigated. It is shown that every closed interval in this order is shellable, those closed intervals which are lattices are characterized and their zeta polynomials are computed. Moreover, using the notion of strong constructibility, it is proved that the order ideal generated by the Coxeter elements of $B_n$ is homotopy Cohen-Macaulay and the Euler characteristic of the order complex of the proper part of this ideal is computed. Finally, an example of a non Cohen-Macaulay closed interval in the absolute order on the group $D_4$ is given and the closed intervals of $D_n$ which are lattices are characterized. Nous étudions l'ordre absolu sur le groupe hyperoctahédral $B_n$. Nous montrons que chaque intervalle fermé de cet ordre est shellable, caractérisons les treillis parmi ces intervalles et calculons les polynômes zêta de ces derniers. De plus, en utilisant la notion de constructibilité forte, nous prouvons que l'idéal engendré par les éléments de Coxeter de $B_n$ est Cohen-Macaulay pour l'homotopie, et nous calculons la caractéristique d'Euler du complexe associé à cet idéal. Pour finir, nous exhibons un exemple d'intervalle fermé non Cohen-Macaulay dans l'ordre absolu du groupe $D_4$, et caractérisons les intervalles fermés de $D_n$ qui sont des treillis.

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