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Abstract: this paper is to illustrate the use of a well-known technique of algebraic topology, the Hopf trace formula, as a tool in computing homology representations of posets. Inspired by a recent paper of Bjorner and Lov'asz ([BL]), we apply this tool to derive information about the homology representation of the symmetric group Sn on a class of subposets of the partition lattice \Pi n : The majority of these subposets are not Cohen-Macaulay. Techniques for such computations have taken on an added... (Update)
Context of citations to this paper: More
...not pure and that is where the difficulty lies in computing the homology representations of the general k mod d partition posets. In [Su2], Sundaram gives a formula for the virtual representation of the symmetric group on the alternating sum of homology of the k mod d...
...left open. This is equivalent to asking whether shellability is preserved by taking the reduced product of two bounded posets (as defined in [Su]) The upper reduced product of bounded posets P 1 and P 2 is defined to be the poset obtained by attaching a top 1 to (P 1 Gamma f...
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BibTeX entry: (Update)
S. Sundaram, Applications of the Hopf trace formula to computing homology representations, Contemp. Math. 178 (1994), 277--309. http://citeseer.ist.psu.edu/sundaram94applications.html More
@misc{ sundaram94applications,
author = "S. Sundaram",
title = "Applications of the Hopf trace formula to computing homology representations",
text = "S. Sundaram, Applications of the Hopf trace formula to computing homology
representations, Contemp. Math. 178 (1994), 277--309.",
year = "1994",
url = "citeseer.ist.psu.edu/sundaram94applications.html" }
Citations (may not include all citations):492 Symmetric functions and Hall polynomials (context) - Macdonald - 1979
211 The Representation Theory of the Symmetric Group (context) - James, Kerber - 1981
178 Elements of Algebraic Topology (context) - Munkres - 1984
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50 Wadsworth and BrookCole (context) - Combinatorics, Wadsworth et al. - 1986
37 Shellable nonpure complexes and posets (context) - Bjorner, Wachs
37 Homotopy Properties of the Poset of Nontrivial p-Subgroups o.. (context) - Quillen - 1978
37 Some Aspects of Groups Acting on Finite Posets (context) - Stanley - 1982
30 Shellable and Cohen-Macaulay Partially Ordered Sets (context) - Bjorner - 1980
28 manifolds and related partition lattices (context) - Bjorner, Welker et al. - 1992
27 subspace arrangements and Mobius functions (context) - Bjorner, Lov'asz et al.
26 The cohomology ring of the colored braid group (context) - Arnold - 1969
22 the Action of the Symmetric Group on the Cohomology of the C.. (context) - Lehrer, Solomon - 1986
22 The homology representations of the symmetric group on Cohen.. - Sundaram - 1994
21 equal partition lattice (context) - Sundaram, Wachs et al. - 1994
18 Whitney numbers of geometric lattices (context) - Baclawski - 1975
14 Ergebnisse der Mathematik und ihrer Grenzgebiete (context) - Goresky, MacPherson et al. - 1988
13 Partitions with restricted block sizes (context) - Linusson - 1994
13 Partitions into even and odd block size and some unusual cha.. (context) - Calderbank, Hanlon et al. - 1986
8 Algebra Universalis (context) - homology, lattices - 1982
8 Group actions on linear subspace arrangements and applicatio.. (context) - Sundaram, Welker - 1994
6 Cohen-Macaulay Connectivity and Geometric Lattices (context) - Baclawski - 1982
6 Shellability of Exponential Structures (context) - Sagan - 1986
3 Fixed points in partially ordered sets (context) - Baclawski, Bjorner - 1979
2 st European Congress Math (context) - arrangements - 1992
2 A basis for the homology of the d-divisible lattice (context) - Wachs - 1992
1 mail address: sheila@paris-gw (context) - Walker, of et al. - 1988
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