Skip to main content
Log in

Two families of Newman lattices

  • Published:
algebra universalis Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. Aschbacher, M., et al. (eds.)Proceedings Rutgers Group Theory Year, 1984–1985. Cambridge Univ. Press, 1984.

  2. Birkhoff, G.,Lattice Theory, 3rd ed. Providence, AMS 1967.

    Google Scholar 

  3. Birkhoff, G.,Selected Papers on Algebra and Topology, G.-C. Rota and J. Oliveira, (eds.), Boston, Birkhäuser, 1987.

    Google Scholar 

  4. Björner, A. andWachs, M.,Bruhat order of Coxeter groups and shellability, Advances in Math.43 (1982), 87–100.

    Google Scholar 

  5. Björner, A.,Orderings of Coxeter groups inCombinatorics and algebra, Curtis Greene (ed.), Am. Math. Soc.43 (1984). (Contemporary Mathematics Series).

  6. Catalan, E.,Note sur une équation aux différences finies, J. de math. pures appl3 (1838), 508–16. (See also ibid.,4 (1839), 91–4, and thepreceding note by Binet).

    Google Scholar 

  7. Coxeter, H. S. M. andMoser, W. O. J.,Generators and Relations for Discrete Groups, 4th ed., Springer, 1980.

  8. Dershowitz, N. (ed.),Rewriting Techniques and Applications. Lecture Notes in Computer Science, #355, Springer, 1989.

  9. Friedman, H. andTamari, D.,Problemes d'associativité ..., J. Comb. Thy.2 (1967), 215–42.

    Google Scholar 

  10. Grätzer, G.,General Lattice Theory. Pure and Applied Mathematics, v. 75, New York, Academic Press, 1978.

    Google Scholar 

  11. Huang, S. andTamari, D.,A simple proof for the lattice property, J. Comb Thy.A13 (1972), 7–13.

    Google Scholar 

  12. Knuth, D.,The Art of Computer Programming, v. 1.Algorithms. Addison Wesley, 1973.

  13. Knuth, D. andBendix, in pp. 263–98 of John Leech (ed.),Computational Problems in Abstract Algebra, Pergamon, 1970.

  14. Lamé, G.,Extrait d'une lettre der M. Lamé à M. Liouville sur cette question: un polygone convexe étant donné ..., J. de math. pures appl.3 (1838) 507–7.

    Google Scholar 

  15. Mardowsky, G.,Primes, irreducibles and extremal lattices, Order9 (1992), 265–90.

    Google Scholar 

  16. Markowsky, G.,Permutation lattices revisited, Math. Soc. Sci.27 (1994), 59–72.

    Google Scholar 

  17. Moore, E. H.,Concerning the abstract groups of order k!and 1/2k!holohedrically isomorphic with the symmetric group and the alternating substitution-groups on k letters, Proc. London Math. Soc.28 (1896), 357–66.

    Google Scholar 

  18. Newman, M. H. A.,On theories with a combinatorial definition of equivalence, Annals of Math.43 (1942), 223–43.

    Google Scholar 

  19. Stanley, R. P.,Enumerative Combinatorics. Wadsworth, 1986.

  20. Yanagimoto, T. andOkamoto, M.,Partial orderings of permutations and monotonicity of a rank correlation statistic, Ann. Inst. Statist. Math.21 (1969), 489–506.

    Google Scholar 

  21. Guilbaud, G. T. andRosenstiehl, P.,Analyse algebrique d'un scrutin, Math. et. Sci. Humanes4 (1963), 10–33. See alsoOrdres Totaux Finis. mathematiques et Sciences de l'Homme XII. Paris, Gauthier-Villars, 1971.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Dedicated to Bjarni Jonsson on his seventieth birthday

This paper has evolved from a talk given by one of us in 1989 (see [8, p. 1]) at a meeting on “term rewriting”. There Chrishan Choffut, Dieter Hofbauer, and Clemens Lautemann suggested Catalan's construction (see §7) after seeing a version of Figure 6.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bennett, M.K., Birkhoff, G. Two families of Newman lattices. Algebra Universalis 32, 115–144 (1994). https://doi.org/10.1007/BF01190819

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01190819

Navigation