Arkiv för Matematik

The finite antichain property in Coxeter groups

Axel Hultman

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We prove that the weak order on an infinite Coxeter group contains infinite antichains if and only if the group is not affine.

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Ark. Mat., Volume 45, Number 1 (2007), 61-69.

Received: 12 December 2005
First available in Project Euclid: 31 January 2017

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2007 © Institut Mittag-Leffler


Hultman, Axel. The finite antichain property in Coxeter groups. Ark. Mat. 45 (2007), no. 1, 61--69. doi:10.1007/s11512-006-0028-3.

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  • Björner, A., Orderings of Coxeter groups, in Combinatorics and Algebra (Boulder, CO 1983), Contemp. Math. 34, pp. 175–195, American Mathematical Society, Providence, RI, 1984.
  • Björner, A. and Brenti, F., Combinatorics of Coxeter groups, Grad. Texts Math. 231, Springer, New York, 2005.
  • Bott, R., An application of the Morse theory to the topology of Lie-groups, Bull. Soc. Math. France 84 (1956), 251–281.
  • Brink, B. and Howlett, R., A finiteness property and an automatic structure for Coxeter groups, Math. Ann. 296 (1993), 179–190.
  • Davis, M. W. and Shapiro, M. D., Coxeter groups are almost convex, Geom. Dedicata 39 (1991), 55–57.
  • Deodhar, V. V., On the root system of a Coxeter group, Comm. Algebra 10 (1982), 611–630.
  • Eriksson, H., Computational and Combinatorial Aspects of Coxeter Groups, Ph.D. thesis, Royal Institute of Technology, Stockholm, 1994.
  • Headley, P., Reduced Expressions in Infinite Coxeter Groups, Ph.D. thesis, University of Michigan, Ann Arbor, MI, 1994.
  • Higman, G., Ordering by divisibility in abstract algebras, Proc. London Math. Soc. (3) 2 (1952), 326–336.
  • Humphreys, J. E., Reflection Groups and Coxeter Groups, Cambridge Univ. Press, Cambridge, 1990.
  • Kruskal, J. B., The theory of well-quasi-ordering, J. Combin. Theory Ser. A 13 (1972), 297–305.
  • Lannér, F., On complexes with transitive groups of automorphisms, Comm. Sém. Math. Univ. Lund 11 (1950), 71pp.
  • Tits, J., Le problème des mots dans les groupes de Coxeter, Symposia Mathematica (INDAM, Rome, 1967/68), vol. 1, pp. 175–185, Academic Press, London, 1969.