Robert, 2D or 3D lattice? Wouter ----- Original Message ----- From: "Robert Munafo" <mrob27@gmail.com> To: "math-fun" <math-fun@mailman.xmission.com> Sent: Saturday, May 07, 2011 6:35 PM Subject: Re: [math-fun] Convex polyominoes
My program is correctly generating the polyominoes (verified by comparing counts to A000105), but I'm stuck (in my mind) on how to derive the convex hull and how to test other points in the grid to see of they are inside or outside the convex hull. Once I know which points define the vertices of the convex hull, I could use the Jordan Curve theorem for testing other points, but when a point falls right on the boundary I have to worry about round-off error.
Any hints?
Allan Wechsler wrote:
On a previous occasion, I talked about enumerating "disklike" polyominoes, polyominoes which occurred as the intersection between a disk and a square lattice. Today I tried counting polyominoes which occurred as the intersection between any convex figure and the lattice. This implies that the convex hull of the polyomino (viewed as a set of lattice points) includes no additional lattice points.
I call these polyominoes "convex", but apparently the term has already been taken by a different class, so I don't know what we should really call them.
Starting from the monomino, the counts seem to be 1, 1, 2, 5, 10, 25. The sequence is not in OEIS, though I confess some uncertainty about the 25 convex hexominoes, and would like confirmation.
-- 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
__________ NOD32 6102 (20110507) Informatie __________
Dit bericht is gecontroleerd door het NOD32 Antivirus Systeem. http://www.nod32.nl