Geodesic
Pattern avoidance and Boolean elements in the Bruhat order on involutions
Journal of Algebraic Combinatorics, Tome 30 (2009) no. 1, pp. 87-102.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We show that the principal order ideal of an element $w$ in the Bruhat order on involutions in a symmetric group is a Boolean lattice if and only if $w$ avoids the patterns 4321, 45312 and 456123. Similar criteria for signed permutations are also stated. Involutions with this property are enumerated with respect to natural statistics. In this context, a bijective correspondence with certain Motzkin paths is demonstrated.
Keywords: keywords Bruhat order, Boolean involutions, pattern avoidance 
@article{JAC_2009__30_1_a2,
     author = {Hultman, Axel and Vorwerk, Kathrin},
     title = {Pattern avoidance and {Boolean} elements in the {Bruhat} order on involutions},
     journal = {Journal of Algebraic Combinatorics},
     pages = {87--102},
     publisher = {mathdoc},
     volume = {30},
     number = {1},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2009__30_1_a2/}
}
TY  - JOUR
AU  - Hultman, Axel
AU  - Vorwerk, Kathrin
TI  - Pattern avoidance and Boolean elements in the Bruhat order on involutions
JO  - Journal of Algebraic Combinatorics
PY  - 2009
SP  - 87
EP  - 102
VL  - 30
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JAC_2009__30_1_a2/
LA  - en
ID  - JAC_2009__30_1_a2
ER  - 
%0 Journal Article
%A Hultman, Axel
%A Vorwerk, Kathrin
%T Pattern avoidance and Boolean elements in the Bruhat order on involutions
%J Journal of Algebraic Combinatorics
%D 2009
%P 87-102
%V 30
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JAC_2009__30_1_a2/
%G en
%F JAC_2009__30_1_a2
Hultman, Axel; Vorwerk, Kathrin. Pattern avoidance and Boolean elements in the Bruhat order on involutions. Journal of Algebraic Combinatorics, Tome 30 (2009) no. 1, pp. 87-102. http://geodesic.mathdoc.fr/item/JAC_2009__30_1_a2/