Doubly stochastic matrices and the Bruhat order
Richard A. Brualdi; Geir Dahl; Eliseu Fritscher
Czechoslovak Mathematical Journal (2016)
- Volume: 66, Issue: 3, page 681-700
- ISSN: 0011-4642
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topBrualdi, Richard A., Dahl, Geir, and Fritscher, Eliseu. "Doubly stochastic matrices and the Bruhat order." Czechoslovak Mathematical Journal 66.3 (2016): 681-700. <http://eudml.org/doc/286797>.
@article{Brualdi2016,
abstract = {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.},
author = {Brualdi, Richard A., Dahl, Geir, Fritscher, Eliseu},
journal = {Czechoslovak Mathematical Journal},
keywords = {Bruhat order; doubly stochastic matrix; face},
language = {eng},
number = {3},
pages = {681-700},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Doubly stochastic matrices and the Bruhat order},
url = {http://eudml.org/doc/286797},
volume = {66},
year = {2016},
}
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
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 66
IS - 3
SP - 681
EP - 700
AB - 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.
LA - eng
KW - Bruhat order; doubly stochastic matrix; face
UR - http://eudml.org/doc/286797
ER -
References
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