A Combinatorial Characterization of Coxeter Groups

2009 ◽  
Vol 23 (1) ◽  
pp. 319-332 ◽  
Author(s):  
Mario Marietti
Keyword(s):  
Coxeter Groups ◽  
Combinatorial Characterization

scholarly journals Tight Quotients and Double Quotients in the Bruhat Order

10.37236/1871 ◽  
2005 ◽  
Vol 11 (2) ◽  
Author(s):  
John R. Stembridge
Keyword(s):  
Coxeter Groups ◽  
Upper Bounds ◽  
Bruhat Order ◽  
Weyl Groups ◽  
Order Dimension ◽  
Parabolic Subgroups ◽  
Affine Weyl Groups ◽  
Positive Side ◽  
Maximal Parabolic Subgroups

It is a well-known theorem of Deodhar that the Bruhat ordering of a Coxeter group is the conjunction of its projections onto quotients by maximal parabolic subgroups. Similarly, the Bruhat order is also the conjunction of a larger number of simpler quotients obtained by projecting onto two-sided (i.e., "double") quotients by pairs of maximal parabolic subgroups. Each one-sided quotient may be represented as an orbit in the reflection representation, and each double quotient corresponds to the portion of an orbit on the positive side of certain hyperplanes. In some cases, these orbit representations are "tight" in the sense that the root system induces an ordering on the orbit that yields effective coordinates for the Bruhat order, and hence also provides upper bounds for the order dimension. In this paper, we (1) provide a general characterization of tightness for one-sided quotients, (2) classify all tight one-sided quotients of finite Coxeter groups, and (3) classify all tight double quotients of affine Weyl groups.

scholarly journals A Combinatorial Characterization of Jacobi Forms

2009 ◽  
Vol 39 (2) ◽  
pp. 455-462
Author(s):  
Youngju Choie ◽  
Olav K. Richter
Keyword(s):  
Jacobi Forms ◽  
Combinatorial Characterization

scholarly journals A combinatorial characterization of planar 2-complexes

1981 ◽  
Vol 44 (2) ◽  
pp. 241-247 ◽  
Author(s):  
Jonathan L. Gross ◽  
Ronald H. Rosen
Keyword(s):  
Combinatorial Characterization

A combinatorial characterization of treelike resolution space

2003 ◽  
Vol 87 (6) ◽  
pp. 295-300 ◽  
Author(s):  
Juan Luis Esteban ◽  
Jacobo Torán
Keyword(s):  
Combinatorial Characterization
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