Bounds on the k-dimension of Products of Special Posets

Trotter conjectured that dimP×Q≥dimP+dimQ−2 for all posets P and Q. To shed light on this, we study the k-dimension of products of finite orders. For k ∈ o(ln n), the value 2dimk(P)−dimk(P×P) is unbounded when P is an n-element antichain, and 2dim2(mP)−dim2(mP×mP) is unbounded when P is a fixed pose...

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Bibliographic Details
Main Authors: Baym, Michael Hartmann, West, Douglas B.
Other Authors: Massachusetts Institute of Technology. Department of Mathematics
Format: Article
Language:en_US
Published: Springer Science+Business Media 2014
Online Access:http://hdl.handle.net/1721.1/85844
https://orcid.org/0000-0003-1303-5598