ISSN:
1572-9273
Keywords:
06A10
;
Order dimension
;
Ferrers dimension
;
Cartesian product
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract It is known that for incidence structures $$\mathbb{K}$$ and $$\mathbb{L}$$ , max $$\{ f{\text{ dim }}\mathbb{K}{\text{, }}f{\text{ dim }}\mathbb{L}{\text{\} }} \leqslant {\text{ }}f{\text{ dim }}\mathbb{K}{\text{ }}x{\text{ }}\mathbb{L} \leqslant f{\text{ dim }}\mathbb{K}{\text{ + }}f{\text{ dim }}\mathbb{L}$$ , wheref dim stands for Ferrers relation. We shall show that under additional assumptions on $$\mathbb{K}$$ and $$\mathbb{L}$$ , both bounds can be improved. Especially it will be shown that the square of a three-dimensional ordered set is at least four-dimensional.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00563528
Permalink
