Timeline for Limit shape for fixed-perimeter lattice polygons
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 28, 2017 at 15:25 | answer | added | john mangual | timeline score: 2 | |
| Apr 28, 2017 at 12:04 | history | edited | Joseph O'Rourke | CC BY-SA 3.0 |
Image links broken; now fixed.
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| Dec 2, 2011 at 12:39 | answer | added | Vincent Beffara | timeline score: 7 | |
| Nov 30, 2011 at 22:03 | answer | added | Nathanael Berestycki | timeline score: 4 | |
| Nov 30, 2011 at 2:29 | comment | added | Joseph O'Rourke | @Mark: Thanks for the key term "van Kampen diagrams" (which I did not know) and the reference, which I will explore! | |
| Nov 30, 2011 at 2:23 | comment | added | user6976 | What you are constructing is van Kampen diagrams over the grouppresentation $ab=ba$. Your moves amount to adding and removing cells (squares) of the diagram. Random diagrams have been considered, say, here: Myasnikov, Alexei; Ushakov, Alexander Random van Kampen diagrams and algorithmic problems in groups. Groups Complex. Cryptol. 3 (2011), no. 1, 121–185. Random diagrams do look "spidery". | |
| Nov 30, 2011 at 1:49 | comment | added | Joseph O'Rourke | @Mark: Thanks for catching that; fixed the corner-pop move. I didn't explain the other move well: it pushes a 3-edge tab down to one edge, and elsewhere pops up an edge to a 3-edge tab. Cool idea to view it as symbol rewriting and limit words! Thanks! | |
| Nov 30, 2011 at 1:26 | comment | added | user6976 | I think the first picture is not correct (?) and the second rule changes perimeter (?). One possible idea is to represent a configuration as a word ($a^{\pm 1}$ for horizontal edges, $b^{\pm 1}$ for vertical edges). Your substitutions give some rewriting rules $ba\leftrightarrow ab$, (if I understand your first rule correctly) and $a\leftrightarrow bab^{-1}$, $b\leftrightarrow aba^{-1}$, and you want to look at the limit words. | |
| Nov 30, 2011 at 0:51 | history | asked | Joseph O'Rourke | CC BY-SA 3.0 |