A basis for the homology of the d-divisible partition lattice

Advances in Mathematics

Volumn 117, Issue 2, 1996, Pages 294-318

  Wachs, Michelle L ^a  

^a Department of Biology   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030577684     PISSN: 00018708     EISSN: None     Source Type: Journal    
DOI: 10.1006/aima.1996.0014     Document Type: Article

References (31)

1. [BG] K. BACLAWSKI AND A. M. GARSIA, Combinatorial decompositions of a class of rings, Adv. in Math. 39 (1981), 155-184.
2. [Ba] H. BARCELO, On the action of the symmetric group on the free Lie algebra and the partition lattice, J. Combin. Theory Ser. A 55 (1990), 93-129.
3. [Bj1] A. BJÖRNER, Shellable and Cohen-Macaulay partially ordered sets, Trans. Amer. Math. Soc. 260 (1980), 159-183.
4. [Bj2] A. BJÖRNER, On the homology of geometric lattices, Algebra Universalis 14 (1982), 107-128.
5. [Bj3] A. BJÖRNER, Homology and shellability of geometric lattices, in "Matroid Applications" (N. White, Ed.), pp. 226-283, Cambridge Univ. Press, Cambridge, 1992.
6. [Bj4] A. BJÖRNER, Some combinatorial and algebraic properties of Coxeter complexes and Tits building, Adv. in Math. 52 (1984), 173-212.
7. [BGS] A. BJÖRNER, A. M. GARSIA, AND R. P. STANLEY, An introduction to Cohen-Macaulay partially ordered sets, in "Ordered Sets" (I. Rival, Ed.), pp. 583-615, Reidel, Dordrecht, 1982.
8. [BL] A. BJÖRNER AND L. LOVÁSZ, Linear decision trees, subspace arrangements and Möbius functions, J. Amer. Math. Soc. 7 (1994), 677-706.
9. [BW1] A. BJÖRNER AND M. L. WACHS, On lexicographically shellable posets, Trans. Amer. Math. Soc. 277 (1983), 323-341.
10. [BW2] A. BJÖRNER AND M. L. WACHS, Shellable nonpure complexes and posets, I, preprint, 1994; Trans. Amer. Math. Soc., to appear.
11. [BWe] A. BJÖRNER AND V. WELKER, The homology of "k-equal" manifolds and related partition lattices, Adv. in Math. 110 (1995), 277-313.
12. [CHR] A. R. CALDERBANK, P. HANLON, AND R. W. ROBINSON, Partitions into even and odd block size and some unusual characters of the symmetric groups, Proc. London Math. Soc. (3) 53 (1986), 288-320.
13. [F] J. FOLKMAN, The homology groups of a lattice, J. Math. Mech. 15 (1966), 631-636.
14. [G] A. M. GARSIA, Combinatorial methods in the theory of Cohen-Macaulay rings, Adv. in Math. 38 (1980), 229-266.
15. [GW] A. M. GARSIA AND M. L. WACHS, Combinatorial aspects of skew representations of the symmetric group, J. Combin. Theory Ser. A 50 (1989), 47-81.
16. [HW] P. HANLON AND M. L. WACHS, On Lie k-algebras, Adv. in Math. 113 (1995), 206-236.
17. [Ja] G. D. JAMES, "The Representation Theory of the Symmetric Groups," Springer Lecture Notes, Vol. 682, Springer-Verlag, Berlin/Heidelberg/New York, 1978.
18. [JK] G. D. JAMES AND A. KERBER, The representation theory of the symmetric group, in "Encyclopedia of Math.," Vol. 16, Addison-Wesley, Reading, MA, 1981.
19. [Jo] A. JOYAL, "Foncteurs analytiques et espèces de structure," Springer Lecture Notes, Vol. 1234, Springer-Verlag, Berlin/Heidelberg/New York, 1986.
20. [K] A. A. KLYACHCO, Lie elements in the tensor algebra, Siberian Math. J. 15 (1974), 1296-1304.
21. [M] J. R. MUNKRES, "Elements of Algebraic Topology," Benjamin/Cummings, Menlo Park, CA, 1984.
22. [Sa] B. E. SAGAN, Shellability of exponential structures, Order 3 (1986), 47-54.
23. [SW] A. SANDERS AND M. L. WACHS, The (co)homology of the lattice of partitions with lower bounded block size, in preparation.
24. [St1] R. P. STANLEY, Exponential structures, Studies Appl. Math. 59 (1978), 73-82.
25. [St2] R. P. STANLEY, Some aspects of groups acting on finite posets, J. Combin. Theory Ser. A 32 (1982), 132-161.
26. [Su1] S. SUNDARAM, The homology representations of the symmetric group on Cohen-Macaulay subposets of the partition lattice, Adv. in Math. 104 (1994), 255-296.
27. [Su2] S. SUNDARAM, Applications of the Hopf trace formula to computing homology representations, in "Proceedings of Jerusalem Combinatorics Conference, 1993" (H. Barcelo and G. Kalai, Eds.), Contemporary Math., Vol. 178, pp. 277-309, Amer. Math. Soc., Providence, RI, 1994.
28. [SuW] S. SUNDARAM AND M. L. WACHS, The homology representations of the k-equal partition lattice, preprint, 1994; Trans. Amer. Math. Soc., to appear.
29. [SuWe] S. SUNDARAM AND V. WELKER, Group actions on arrangements of linear subspaces and applications to configuration spaces, preprint, 1994; Trans. Amer. Math. Soc., to appear.
30. [W1] M. L. WACHS, On the (co)homology of the partition lattice and the free Lie algebra, preprint, 1994; Discrete Math., to appear.
31. [W2] M. L. WACHS, Whitney homology of semipure shellable posets, in preparation.