Angle Orders
نویسنده
چکیده
A finite poset is an angle order if its points can be mapped into angular regions in the plane so that x precedes y in the poset precisely when the region for x is properly included in the region for y. We show that all posets of dimension four or less are angle orders, all interval orders are angle orders, and that some angle orders must have an angular region less than 180” (or more than 180”). The latter result is used to prove that there are posets that are not angle orders. The smallest verified poset that is not an angle order has 198 points. We suspect that the minimum is around 30 points. Other open problems are noted, including whether there are dimension-5 posets that are not angle orders. AMS (MOS) subject classifications (1980). Primary 06AlO; secondary 06B05,05AOS.
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