Reading, Nathan; Waugh, Debra J. The order dimension of Bruhat order on infinite Coxeter groups. (English) Zbl 1067.20051 Electron. J. Comb. 11, No. 2, Research paper R13, 26 p. (2004). Summary: 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 \(\widetilde A_n\). We also demonstrate that the order dimension of the Bruhat order is infinite for a large class of Coxeter groups. Cited in 1 Document MSC: 20F55 Reflection and Coxeter groups (group-theoretic aspects) 06A07 Combinatorics of partially ordered sets Keywords:order dimensions; Bruhat ordering; affine Coxeter groups PDFBibTeX XMLCite \textit{N. Reading} and \textit{D. J. Waugh}, Electron. J. Comb. 11, No. 2, Research paper R13, 26 p. (2004; Zbl 1067.20051) Full Text: EuDML EMIS