Wouter: We're just in two dimensions at this point; the 3D convex hull problem is much more challenging! Rich: Robert and I are having some backchannel chat about the growth rate. I anticipated that the growth rate might be much slower than that for unrestricted polyominoes, because the convexity constraint imposes lots of local forbidden configurations, which almost all unrestricted polyominoes would be expected to have. If you want to see something amusing and hard to think about, which I did *not* expect, look at the second differences of the sequence Robert gave. See if you can explain the very marked period-2 oscillation. Robert has some ideas about that which I haven't read carefully yet. On Mon, May 9, 2011 at 4:12 PM, <rcs@xmission.com> wrote:
Interesting that the ratio of consecutive terms seems to be < 2, while the ratio for ordinary polyominos is (likely) > 4.
Rich
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Quoting Robert Munafo <mrob27@gmail.com>:
I forgot to give a link -- my web page for the sequence is here:
http://mrob.com/pub/math/seq-a181785.html
On Sun, May 8, 2011 at 01:59, Robert Munafo <mrob27@gmail.com> wrote:
I have now implemented the "disklike polyomino" algorithm [...]
1, 1, 2, 5, 10, 25, 48, 107, 193, 365, 621, 1082, 1715
I have submitted this sequence to OEIS as A181785< http://oeis.org/A181785>
.
I have also created a web page for the sequence, which includes pictures of the "disklike" polyominoes for N=6 and N=7.
-- Robert Munafo -- mrob.com Follow me at: fb.com/mrob27 - twitter.com/mrob_27 - mrob27.wordpress.com- youtube.com/user/mrob143 - rilybot.blogspot.com _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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