A Hodge Decomposition for the Complex of Injective

@inproceedings{Hanlon2003AHD,
  title={A Hodge Decomposition for the Complex of Injective},
  author={P. D. Hanlon and Patricia Hersh},
  year={2003}
}
Reiner and Webb (preprint, 2002) compute the Sn-module structure for the complex of injective words. This paper refines their formula by providing a Hodge type decomposition. Along the way, this paper proves that the simplicial boundary map interacts in a nice fashion with the Eulerian idempotents. The Laplacian acting on the top chain group in the complex of injective words is also shown to equal the signed random to random shuffle operator. Uyemura-Reyes, 2002, conjectured that the (unsigned… CONTINUE READING

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Showing 1-10 of 11 references

Stanford University

  • Jay-Calvin Uyemura-Reyes, Random Walk, Semi-Direct Products, Card Shuffling, Ph. D. Thesis
  • May
  • 2002
Highly Influential
8 Excerpts

Loday , Partition Eulerienne et operations en homologie cyclique , C

  • J.-L.
  • 1990

The action of Sn on the components of the Hodge decomposition of Hochschild homology

  • P. Hanlon
  • Michigan Math. J.,
  • 1990

Idempotents for the free Lie algebra and q-enumeration

  • F. Bergeron, N. Bergeron, A. M. Garsia
  • Invariant Theory and Tableaux (Minneapolis, MN,
  • 1988

Loday, Partition Eulerienne et operations en homologie cyclique

  • Lo J.-L
  • C.R. Acad. Sci. Pari Ser. I Math.,
  • 1988

A Hodge-type decomposition for commutative algebra cohomology

  • M. Gerstenhaber, S. D. Schack
  • J. Pure Appl. Algebra,
  • 1987

On lexicographically shellable posets

  • P. Hanlon, R. W. Robinson
  • Trans . Amer . Math . Soc .
  • 1983

Cellular homology for posets

  • F. D. Farmer
  • Math. Japan,
  • 1978

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