Bounds on the k-dimension of Products of Special Posets
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Baym_Bounds on.pdf
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204.01 KB
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Author(s)
Baym, Michael Hartmann
West, Douglas B.
Date Issued
November 2012
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
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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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.
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DOI of Published Version
https://doi.org/10.1007/s11083-012-9276-y
