# 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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- Brualdi, R. A., Hwang, S.-G., A Bruhat order for the class of $(0,1)$-matrices with row sum vector $R$ and column sum vector $S$, Electron. J. Linear Algebra (electronic only) 12 (2004/2005), 6-16. (2004) MR2139456
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