Homotopy of Non-Modular Partitions and the Whitehouse Module

Journal of Algebraic Combinatorics

Volumn 9, Issue 3, 1999, Pages 251-269

  Sundaram, Sheila ^a,b  

^a WESLEYAN UNIVERSITY   (United States)

^b NONE   (United States)

Author keywords

Group representation; Homology; Homotopy; Poset; Set partition

Indexed keywords

EID: 0007219458     PISSN: 09259899     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1018648219348     Document Type: Article

References (31)

1. E. Babson, A. Björner, S. Linusson, J. Shareshian, and V. Welker, "Complexes of not i-connected graphs, extended abstract," Proceedings of the 9th Formal Power Series and Algebraic Combinatorics Conference, Vienna, July 1997.
2. K. Baclawski, "Cohen-Macaulay ordered sets," J. Algebra 63 (1980), 226-258.
3. K. Baclawski, "Cohen-Macaulay connectivity and geometric lattices," Europ. J. Combinatorics 3 (1982), 293-305.
4. D.J. Benson, Representations and Cohomology, Cambridge University Press, 1992, Vol. 2.
5. A. Björner, "Shellable and Cohen-Macaulay partially ordered sets," Trans. Amer. Math. Soc. 260 (1980), 159-183.
6. A. Björner, "Some combinatorial and algebraic properties of coxeter complexes and tits buildings," Adv. Math. 52 (1984), 173-212.
7. A. Björner, "Subspace arrangements," Proc. First European Congress of Mathematics, Paris 1992, Birkhaüser, Basel, pp. 321-370, 1994.
8. A. Björner, "Topological methods," in Handbook of Combinatorics, R. Graham, M. Grötschel and L. Lóvasz (Eds.), North-Holland, 1995, pp. 1819-1872.
9. A. Björner and M.L. Wachs, "Shellable nonpure complexes and posets I," Trans. Amer. Math. Soc. 348(4) (1996), 1299-1327.
10. S. Bouc, "Homologie de certains ensembles de 2-sous-groupes du groupe symétrique," J. Algebra 150 (1992), 158-186.
11. E. Getzler and M. Kapranov, "Cyclic operads and cyclic homology," Geometry, Topology and Physics, International Press, Cambridge, MA, 1995, pp. 167-201.
12. P. Hanlon, "The fixed-point partition lattices," Pacific J. Math. 96 (1981), 319-341.
13. P. Hanlon, "Otter's method and the homology of homeomorphically irreducible k-trees," J. Comb. Theory (A) 74(2) (1996), 301-320.
14. P. Hanlon and R.P. Stanley, "A q-deformation of a trivial symmetric group action," Trans. Amer. Math. Soc. 350 (1998), 4445-4459.
15. D. Kozlov, "General lexicographic shellability and orbit arrangements," preprint (1996), annals of combinatorics, to appear.
16. n+1-actions," Commun. Math. Phys. 176 (1996), 467-474.
17. J. R. Munkres, Elements of Algebraic Topology, Addison-Wesley, 1984.
18. J.R. Munkres, "Topological results in combinatorics," Mich. Math. J. 31 (1984), 113-128.
19. D. Quillen, "Homotopy properties of the poset of nontrivial p-subgroups of a group," Adv. Math. 28 (1978), 101-128.
20. Alan Robinson, "The space of fully grown trees," Sonderforschungsbereich 343, Universität Bielefeld, Preprint 92-083 (1992).
21. n+1," J. Pure and Appl. Algebra 111(1-3) (1996), 245-253.
22. L. Solomon, "A decomposition of the group algebra of a finite Coxeter group," J. Algebra 9 (1968), 220-239.
23. R.P. Stanley, "Balanced Cohen-Macaulay complexes," Trans. Amer. Math. Soc. 249 (1979), 139-157.
24. R.P. Stanley, "Some aspects of groups acting on finite posets," J. Comb. Theory (A) 32(2) (1982), 132-161.
25. R.P. Stanley, Enumerative Combinatorics, Wadsworth and Brooks/Cole, Pacific Grove, CA, 1986, Vol. 1.
26. S. Sundaram, "The homology representations of the symmetric group on Cohen-Macaulay subposets of the partition lattice," Adv. in Math. 104(2) (1994), 225-296.
27. S. Sundaram, "Homotopy and homology of non-modular partitions and related posets, extended abstract," Proceedings of the 9th Formal Power Series and Algebraic Combinatorics Conference, Vienna, July 1997.
28. M.L. Wachs, "A basis for the homology of the d-divisible partition lattice," Adv. in Math. 117(2) (1996), 294-318.
29. J.W. Walker, "Topology and combinatorics of ordered sets," Ph.D. Thesis, Massachusetts Institute of Technology, 1981.
30. J.W. Walker, "Homotopy type and Euler characteristic of partially ordered sets," Europ. J. Combinatorics 2 (1981), 373-384.
31. S.A. Whitehouse, "Γ-(Co)homology of commutative algebras and some related representations of the symmetric group," Ph.D. Thesis, University of Warwick, 1994.