Bounds on the k-dimension of Products of Special Posets

Author(s)
Baym, Michael Hartmann; West, Douglas B.
Thumbnail
DownloadBaym_Bounds on.pdf (204.0Kb)
PUBLISHER_POLICY
Terms of use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Metadata
Show full item record
Abstract
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 poset with unique maximum and minimum. For products of the “standard” orders S m and S n of dimensions m and n, dimk(Sm×Sn)=m+n−min{2,k−2} . For higher-order products of “standard” orders, dim2(∏ti=1Sni)=∑ni if each n i  ≥ t.
Date issued
2012-11
URI
http://hdl.handle.net/1721.1/85844
Department
Massachusetts Institute of Technology. Department of Mathematics
Journal
Order
Publisher
Springer Science+Business Media
Citation
Baym, Michael, and Douglas B. West. “Bounds on the k-Dimension of Products of Special Posets.” Order 30, no. 3 (November 2013): 779–796.
Version: Author's final manuscript
ISSN
0167-8094
1572-9273
Collections