Geodesic
Doubly stochastic matrices and the Bruhat order
Czechoslovak Mathematical Journal, Tome 66 (2016) no. 3, pp. 681-700

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

The Bruhat order is defined in terms of an interchange operation on the set of permutation matrices of order $n$ which corresponds to the transposition of a pair of elements in a permutation. We introduce an extension of this partial order, which we call the stochastic Bruhat order, for the larger class $\Omega _n$ of doubly stochastic matrices (convex hull of $n\times n$ permutation matrices). An alternative description of this partial order is given. We define a class of special faces of $\Omega _n$ induced by permutation matrices, which we call Bruhat faces. Several examples of Bruhat faces are given and several results are presented.
DOI : 10.1007/s10587-016-0286-6
Classification : 05B20, 06A07, 15B51
Keywords: Bruhat order; doubly stochastic matrix; face 
@article{10_1007_s10587_016_0286_6,
     author = {Brualdi, Richard A. and Dahl, Geir and Fritscher, Eliseu},
     title = {Doubly stochastic matrices and the {Bruhat} order},
     journal = {Czechoslovak Mathematical Journal},
     pages = {681--700},
     publisher = {mathdoc},
     volume = {66},
     number = {3},
     year = {2016},
     doi = {10.1007/s10587-016-0286-6},
     mrnumber = {3556861},
     zbl = {06644027},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10587-016-0286-6/}
}
TY  - JOUR
AU  - Brualdi, Richard A.
AU  - Dahl, Geir
AU  - Fritscher, Eliseu
TI  - Doubly stochastic matrices and the Bruhat order
JO  - Czechoslovak Mathematical Journal
PY  - 2016
SP  - 681
EP  - 700
VL  - 66
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1007/s10587-016-0286-6/
DO  - 10.1007/s10587-016-0286-6
LA  - en
ID  - 10_1007_s10587_016_0286_6
ER  - 
%0 Journal Article
%A Brualdi, Richard A.
%A Dahl, Geir
%A Fritscher, Eliseu
%T Doubly stochastic matrices and the Bruhat order
%J Czechoslovak Mathematical Journal
%D 2016
%P 681-700
%V 66
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1007/s10587-016-0286-6/
%R 10.1007/s10587-016-0286-6
%G en
%F 10_1007_s10587_016_0286_6
Brualdi, Richard A.; Dahl, Geir; Fritscher, Eliseu. Doubly stochastic matrices and the Bruhat order. Czechoslovak Mathematical Journal, Tome 66 (2016) no. 3, pp. 681-700. doi: 10.1007/s10587-016-0286-6

Cité par Sources :