A Class of Lattices Whose Intervals are Spherical or Contractible

Author: Linusson S.

Source: European Journal of Combinatorics, Volume 20, Number 3, April 1999 , pp. 239-257(19)

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Abstract:

We study a class of lattices called weak^*complemented lattices which are shown to have the property that the order complex of any interval of the lattice is either contractible or homotopy equivalent to a sphere. The two main examples are lattices generated by intervals in a total order and the lattices of partitions of integers under dominance order. The proofs are done mainly using homotopy complementation formulas for lattices and with a method called B-labeling. We also show that a class of lattices called Greene lattices are either contractible or spherical. Lattices generated by multisets are also discussed.Copyright 1999 Academic Press

Language: English

Document Type: Research article

Affiliations: Department of Mathematics, Stockholms Universitet, 91 Stockholm, S-106, Sweden

Publication date: 1999-04-01