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

[1] Björner, A., Brenti, F.: Combinatorics of Coxeter Groups. Graduate Texts in Mathematics 231 Springer, New York (2005). | MR | Zbl

[2] Björner, A., Brenti, F.: An improved tableau criterion for Bruhat order. Electron. J. Comb. 3 Research paper R22, 5 pages (1996), printed version J. Comb. 3 311-315 (1996). | MR | Zbl

[3] Brualdi, R. A.: Combinatorial Matrix Classes. Encyclopedia of Mathematics and Its Applications 108 Cambridge University Press, Cambridge (2006). | MR | Zbl

[4] Brualdi, R. A., Dahl, G.: The Bruhat shadow of a permutation matrix. Mathematical Papers in Honour of Eduardo Marques de Sá Textos de Matemática. Série B 39 Universidade de Coimbra, Coimbra (2006), 25-38. | MR | Zbl

[5] Brualdi, R. A., Deaett, L.: More on the Bruhat order for {$(0,1)$}-matrices. Linear Algebra Appl. 421 (2007), 219-232. | MR | Zbl

[6] 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. | MR

[7] Magyar, P.: Bruhat order for two flags and a line. J. Algebr. Comb. 21 (2005), 71-101. | DOI | MR | Zbl

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