Timeline for Rhombus tilings with more than three directions
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
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| Feb 24, 2023 at 8:53 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
replaced the dead link
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| Jan 18, 2023 at 8:09 | comment | added | Martin Sleziak | A new link for the first one has pid/d3e2ccbac7282af690449c4c286455212331eb86. The second paper is this one or this one. | |
| Jan 18, 2023 at 8:09 | comment | added | Martin Sleziak | The two citeseerx links seem to be dead. Wayback Machine shows that one of them is Quasicommuting families of quantum Plücker coordinates (1998) by Bernard Leclerc , Andrei Zelevinsky and the other one is Zonotopal Tilings and the Bohne-Dress Theorem (1994) by Jürgen Richter-Gebert , Günter M. Ziegler. | |
| Jan 1, 2023 at 13:33 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
http -> https (the question was bumped anyway)
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| Mar 19, 2021 at 22:30 | comment | added | Jeanne Scott | I would add that Leclerc and Zelevinsky showed that maximal (by inclusion) collections of pairwise strongly separated subsets of $[1, \dots, n]$ are in bijection with reduced factorizations of the highest permutation $w_0$ in the symmetric group $S_n$. It is folklore (?) that reduced factorizations of this kind are in one-to-one correspondence with rhombic tilings of a regular $2n$-gon. | |
| Mar 19, 2021 at 21:46 | answer | added | Matthieu Latapy | timeline score: 8 | |
| Apr 10, 2020 at 7:00 | comment | added | Pavel Galashin | a generalization of the strong separation result (to arbitrary oriented matroids, including centrally symmetric polygons) appears in Theorem 2.7 and Proposition 5.1 of arxiv.org/abs/1708.01329 | |
| Nov 9, 2011 at 12:46 | history | edited | David E Speyer | CC BY-SA 3.0 |
added 19 characters in body
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| Nov 9, 2011 at 12:38 | answer | added | Thomas Fernique | timeline score: 3 | |
| Oct 17, 2011 at 18:49 | answer | added | David Eppstein | timeline score: 7 | |
| Oct 17, 2011 at 18:36 | answer | added | Greg Kuperberg | timeline score: 7 | |
| Oct 17, 2011 at 16:03 | comment | added | David Eppstein | A minor correction: simple pseudoline arrangements (where at most two pseudolines meet at any crossing) are the ones dual to rhombus tilings. For non-simple arrangements you get tilings by centrally symmetric polygons that may not themselves be rhombs. And for weak pseudoline arrangements (where the pseudolines that don't cross don't have to form parallel bundles, e.g. like lines in the hyperbolic plane) you still get tilings by centrally symmetric polygons, but of a region that is not necessarily convex — for this last bit, see e.g. my paper arXiv:cs/0406020. | |
| Oct 17, 2011 at 12:32 | history | edited | David E Speyer | CC BY-SA 3.0 |
added 1046 characters in body
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| Oct 17, 2011 at 2:00 | history | asked | David E Speyer | CC BY-SA 3.0 |