ISSN:
1572-9273
Keywords:
06A10
;
06A23
;
Order-dimension
;
Ferrers relation
;
partition lattice
;
linear lattice
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract The aim of this paper is to study the order-dimension of partition lattices and linear lattices. Our investigations were motivated by a question due to Bill Sands: For a lattice L, does dim L=n always imply |L|≥2 n ? We will answer this question in the negative since both classes of lattices mentioned above form counterexamples. In the case of the partition lattices, we will determine the dimension up to an absolute constant. For the linear lattice over GF(2), L n , we determine the dimension up to a factor C/n for an absolute constant C.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00340776
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