Geodesic
The order dimension of Bruhat order on infinite Coxeter groups.
The electronic journal of combinatorics, The Stanley Festschrift volume, Tome 11 (2004) no. 2
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We give a quadratic lower bound and a cubic upper bound on the order dimension of the Bruhat (or strong) ordering of the affine Coxeter group ${\tilde{A}}_n$. We also demonstrate that the order dimension of the Bruhat order is infinite for a large class of Coxeter groups.
DOI : 10.37236/1870
Classification : 20F55, 06A07
Mots-clés : order dimensions, Bruhat ordering, affine Coxeter groups 
@article{10_37236_1870,
     author = {Nathan Reading and Debra J. Waugh},
     title = {The order dimension of {Bruhat} order on infinite {Coxeter} groups.},
     journal = {The electronic journal of combinatorics},
     year = {2004},
     volume = {11},
     number = {2},
     doi = {10.37236/1870},
     zbl = {1067.20051},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1870/}
}
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Nathan Reading; Debra J. Waugh. The order dimension of Bruhat order on infinite Coxeter groups.. The electronic journal of combinatorics, The Stanley Festschrift volume, Tome 11 (2004) no. 2. doi: 10.37236/1870

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