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Roots, games, and automata

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Part of the Graduate Texts in Mathematics book series (GTM, volume 231)

Keywords

Positive Root Simple Root Coxeter Group Dihedral Group Small Root 
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Notes

  1. [11]
    V. I. Arnol’d, Snake calculus and the combinatorics of the Bernoulli, Euler and Springer numbers of Coxeter groups. (Russian) Uspekhi Mat. Nauk 47 (1992), no. 1 (283), 3–45, 240; transl. Russian Math. Surveys 47 (1992), 1–51. [130]MathSciNetGoogle Scholar
  2. [79]
    N. Bourbaki, Groupes et algébres de Lie, Ch. 4–6, Éléments de Mathématique, Fasc. XXXIV, Hermann, Paris, 1968; Masson, Paris, 1981. Ch. 5 [24, 88, 127, 129, 130, 170]Google Scholar
  3. [103]
    B. Brink, The set of dominance-minimal roots, J. Algebra 206 (1998), 371–412. [130]zbMATHMathSciNetCrossRefGoogle Scholar
  4. [104]
    B. Brink, R. Howlett, A finiteness property and an automatic structure for Coxeter groups, Math. Ann. 296 (1993), 179–190. [130]MathSciNetCrossRefGoogle Scholar
  5. [117]
    W. Casselman, Machine calculations in Weyl groups, Invent. Math. 116 (1994), 95–108. [130]zbMATHMathSciNetCrossRefGoogle Scholar
  6. [118]
    W. Casselman, Automata to perform basic calculations in Coxeter groups, Representations of Groups (Banff, AB, 1994), 35–58, CMS Conf. Proc., 16, American Mathematical Society, Providence, RI, 1995. [130]Google Scholar
  7. [119]
    W. Casselman, Computation in Coxeter groups. I. Multiplication. Electron. J. Combin. 9 (2002), RP 25, 22 pp. [130]Google Scholar
  8. [171]
    M. W. Davis, M. D. Shapiro, Coxeter groups are almost convex, Geom. Dedicata 39 (1991), 55–57. [130]MathSciNetCrossRefGoogle Scholar
  9. [179]
    V. V. Deodhar, On the root system of a Coxeter group, Commun. Algebra 10 (1982), 611–630. [64, 130]zbMATHMathSciNetGoogle Scholar
  10. [200]
    M. J. Dyer, Hecke algebras and reflections in Coxeter groups, Ph.D. Thesis, University of Sydney, 1987. [130, 161, 170]Google Scholar
  11. [223]
    H. Eriksson, Computational and combinatorial aspects of Coxeter groups, Ph.D. Thesis, KTH, Stockholm, Sweden, 1994. [88, 125, 130, 294]Google Scholar
  12. [227]
    K. Eriksson, Strongly convergent games and Coxeter groups, Ph.D. Thesis, KTH, Stockholm, Sweden, 1993. [130]Google Scholar
  13. [290]
    P. Headley, Reduced expressions in infinite Coxeter groups, Ph.D. Thesis, University of Michigan, 1994. [130]Google Scholar
  14. [306]
    J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge University Press, Cambridge, 1990. Ch. 5 [4, 24, 123, 124, 126, 130, 132, 134, 136, 174, 175, 200, 205, 240]Google Scholar
  15. [400]
    S. Mozes, Reflection processes on graphs and Weyl groups, J. Combin. Theory, Ser. A 53 (1990), 128–142. [130]zbMATHMathSciNetCrossRefGoogle Scholar
  16. [463]
    J.-Y. Shi, Some numeric results on root systems, Pacific J. Math. 160 (1993), 155–164. [130]zbMATHMathSciNetGoogle Scholar

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