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On the Homology of Distributive Lattices

โœ Scribed by W.F. Doran IV

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
167 KB
Volume
19
Category
Article
ISSN
0195-6698

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โœฆ Synopsis

This paper gives a method for computing the reduced poset homology of the rank-selected subposet of a distributive lattice. As an example of the method, let L be the lattice

S b acts on L by permuting coordinates. For S โŠ† [ab], we give a description of the decomposition of the reduced homology of L S as an S b -module. This generalizes L. Solomon's result for decomposition of the reduced homology of the Boolean algebra (B b ) S as an S b -module.

๐Ÿ“œ SIMILAR VOLUMES

Symplectic Analogs of the Distributive L
Symplectic Analogs of the Distributive Lattices L(m, n)
โœ Robert G. Donnelly ๐Ÿ“‚ Article ๐Ÿ“… 1999 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 244 KB

We introduce two families of symplectic analogs of the distributive lattices L(m, n). We give several combinatorial descriptions of these distributive lattices and use combinatorial methods to produce their rank generating functions. Using Proctor's sl(2, C) technique, we prove that these symplectic