hihi, all - I have some intermediate results from the programs I wrote for the minimum area convex lattice polygon problem Program Results (so far) n min i min a (as found by my program) 11 17 19.5...21.5 15 45 49.5...51.5 17 68 ...75.5 18 79 ...87 19 98 ...106.5 (n=20 has been running for 18h so far; I have no idea how long it will take) I also have a request for information: are there any explicit upper bounds known for n>16 (the limit of the listing in the OEIS web site that I read)? Steve Finch reported a previous upper area bound of 86.5 for n=17, but I did not find that in the OEIS (perhaps I was looking at an older copy that was cached somewhere else). Because the first program was taking way too much time (the run I mentioned before that was supposed to finish Thursday ran through Sunday last week before I killed it after more than 210 CPU hours), I have made two sets of improvements to the program, including using some suggestions from Dylan Thurston and Dan Hoey (thanx to both of you). The time saving is substantial: with these changes, the time for n=15 (with edge length bound = 10) is reduced from 3606.580 CPU seconds to 221.540 CPU seconds, and the time for n=18 (with edge length bound = 10) is reduced from 169103.840 CPU seconds (over 48 hours) to just 6453.330 CPU seconds. More timing details are on the web site. It turns out that the smallest longest edge length for the minimum area polygons is much smaller than the original edge length bound used to find them (of course, there are infinitely many minimum area polygons with longer edge lengths as well), and as far as I've checked, the results do not change when the edge length bound is increased (at least through n=15, with a few larger cases checked and more large cases and comparisons pending). Edge length 5 suffices at least up to n=19 (it means that the edge length bound of 10 that I used is much larger than it needs to be to find at least one likely minimum area polygon). Full details and explanations will eventually show up on the web. For now, you can just look at URL http://www.cs.umd.edu/~cal/convex/ to see the intermediate results (the archive files are fairly small; they each expand to about 2MB). Unfortunately, there is a lock on raw directory listings at Univ. Md., so accessing any of the sub-directories of convex/ will get a 403 error (I forget just now how to change that behavior). In any case, the archive files can be downloaded to get all of the files in all of these sub-directories to examine. more soon, cal