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A short proof thatN3is not a circle containment order

✍ Scribed by Glenn H. Hurlbert

Publisher
Springer Netherlands
Year
1988
Tongue
English
Weight
100 KB
Volume
5
Category
Article
ISSN
0167-8094

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✦ Synopsis

A partially ordered set P is called a circle containment order provided one can assign to each x e P a circle C x so that x <~ y Β’=~ Cx c_ Cy. We show that the infinite three-dimensional poset N 3 is not a circle containment order and note that it is still unknown whether or not [n] 3 is such an order for arbitrarily large n.

πŸ“œ SIMILAR VOLUMES

[2] x [3] xNis not a circle order
[2] x [3] xNis not a circle order
✍ Chiang Lin πŸ“‚ Article πŸ“… 1991 πŸ› Springer Netherlands 🌐 English βš– 233 KB

The result stated in the title is proved in this note. Actually we show that S x N is not a circle order, where S = {( 1, I), (1,2), (1,3), (2, I), (2, 3)}. Furthermore this non-circle order is critical in the sense that (S -{x}) x N is a circle order for any x in S.

Committee reports. Report on patent law
Committee reports. Report on patent law revision**The evidence in support of the Preambles and Resolutions and suggested additions to the copyright, patent and trade-mark laws contained in the first part of our report was not published in the May Journal owing to want of space. I am now sending you the remaining part of the report, by request, as it is considered quite necessary for the members of the Association to have in their hands before the next annual meeting, the entire document for consideration and study. It is believed that this will decidedly facilitate matters and save much time at the annual meeting which otherwise might be used up in unnecessary discussion of the subject.Your Committee wishes to again emphasize that fact that we have no desire to impose our personal views on the Association. The copyright and patent laws were designed to promote progress in science and the useful arts and the trade-mark laws to protect the public from fraud and imposition. It is generally conceded that the laws as now interpreted and applied fall short in accomplishing their purpose. It is therefore incumbent upon the A. Ph. A., representing the pharmacists of America, to suggest proper modifications of the law, of such kind as to secure the very important objects for which they were enacted.β€”F. E. Stewarcth, Chairman.
πŸ“‚ Article πŸ“… 1917 πŸ› Elsevier βš– 359 KB πŸ‘ 1 views