| Title:
|
Doubly stochastic matrices and the Bruhat order (English) |
| Author:
|
Brualdi, Richard A. |
| Author:
|
Dahl, Geir |
| Author:
|
Fritscher, Eliseu |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
66 |
| Issue:
|
3 |
| Year:
|
2016 |
| Pages:
|
681-700 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Bruhat order |
| Keyword:
|
doubly stochastic matrix |
| Keyword:
|
face |
| MSC:
|
05B20 |
| MSC:
|
06A07 |
| MSC:
|
15B51 |
| idZBL:
|
Zbl 06644027 |
| idMR:
|
MR3556861 |
| DOI:
|
10.1007/s10587-016-0286-6 |
| . |
| Date available:
|
2016-10-01T15:16:38Z |
| Last updated:
|
2023-10-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/145865 |
| . |
| Reference:
|
[1] Björner, A., Brenti, F.: Combinatorics of Coxeter Groups.Graduate Texts in Mathematics 231 Springer, New York (2005). Zbl 1110.05001, MR 2133266 |
| Reference:
|
[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). Zbl 0884.05096, MR 1399399 |
| Reference:
|
[3] Brualdi, R. A.: Combinatorial Matrix Classes.Encyclopedia of Mathematics and Its Applications 108 Cambridge University Press, Cambridge (2006). Zbl 1106.05001, MR 2266203 |
| Reference:
|
[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. Zbl 1178.05023, MR 2291012 |
| Reference:
|
[5] Brualdi, R. A., Deaett, L.: More on the Bruhat order for {$(0,1)$}-matrices.Linear Algebra Appl. 421 (2007), 219-232. Zbl 1161.05018, MR 2294337 |
| Reference:
|
[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 2139456 |
| Reference:
|
[7] Magyar, P.: Bruhat order for two flags and a line.J. Algebr. Comb. 21 (2005), 71-101. Zbl 1076.14069, MR 2130795, 10.1007/s10801-005-6281-x |
| . |
