scholarly journals The generalized lifting property of Bruhat intervals

2016 ◽  
Vol 45 (3) ◽  
pp. 687-700 ◽  
Author(s):  
Fabrizio Caselli ◽  
Paolo Sentinelli
Keyword(s):  
Bruhat Intervals

scholarly journals Weak Generalized Lifting Property, Bruhat Intervals, and Coxeter Matroids

2020 ◽  
Author(s):  
Fabrizio Caselli ◽  
Michele D’Adderio ◽  
Mario Marietti
Keyword(s):  
Coxeter Group ◽  
Coxeter Groups ◽  
Combinatorial Properties ◽  
Coxeter Matroid ◽  
Finite Coxeter Group ◽  
Bruhat Intervals

Abstract We provide a weaker version of the generalized lifting property that holds in complete generality for all Coxeter groups, and we use it to show that every parabolic Bruhat interval of a finite Coxeter group is a Coxeter matroid. We also describe some combinatorial properties of the associated polytopes.

scholarly journals From Bruhat intervals to intersection lattices and a conjecture of Postnikov

2009 ◽  
Vol 116 (3) ◽  
pp. 564-580 ◽  
Author(s):  
Axel Hultman ◽  
Svante Linusson ◽  
John Shareshian ◽  
Jonas Sjöstrand
Keyword(s):  
Bruhat Intervals

scholarly journals An Abstract Model for Bruhat Intervals

2000 ◽  
Vol 21 (2) ◽  
pp. 197-222 ◽  
Author(s):  
Fokko du Cloux
Keyword(s):  
Abstract Model ◽  
Bruhat Intervals

scholarly journals Flip Posets of Bruhat Intervals

10.37236/7910 ◽  
2018 ◽  
Vol 25 (4) ◽  
Author(s):  
Saúl A. Blanco
Keyword(s):  
Maximal Chain ◽  
Combinatorial Description ◽  
Bruhat Graph ◽  
Eulerian Posets ◽  
Bruhat Intervals

In this paper we introduce a way of partitioning the paths of shortest lengths in the Bruhat graph $B(u,v)$ of a Bruhat interval $[u,v]$ into rank posets $P_{i}$ in a way that each $P_{i}$ has a unique maximal chain that is rising under a reflection order. In the case where each $P_{i}$ has rank three, the construction yields a combinatorial description of some terms of the complete $\textbf{cd}$-index as a sum of ordinary $\textbf{cd}$-indices of Eulerian posets obtained from each of the $P_{i}$.

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