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The dimension of the cartesian product of posets

✍ Scribed by Chiang Lin

Publisher: Elsevier Science
Year: 1991
Tongue: English
Weight: 775 KB
Volume: 88
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(91)90060-f

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✦ Synopsis

Lin, C., The dimension of the Cartesian product of posets, Discrete Mathematics 88 (1991) 79-92.

We give a characterization of nonforced pairs in the Cartesian product of two posets, and apply this to determine the dimension of P X Q, where P, Q are some subposets of 2" and 2" respectively. One of our results is dim Si x 5': = n + m -2 for n, m 3 3. This generalizes Trotter's result in [5], where he showed that dimSi x St = 2n -2. We also disprove the following conjecture 121: If P, Q are two posets and 0,l E P, then dim P X Q 2 dim P + dim Q -1.

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