Timeline for What rectangles can a set of rectangles tile?
Current License: CC BY-SA 4.0
18 events
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| Dec 24, 2022 at 12:55 | history | edited | YCor |
edited tags
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| Dec 24, 2022 at 8:44 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
http -> https (the question was bumped anyway)
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| Dec 17, 2022 at 4:21 | answer | added | Glenn Sun | timeline score: 4 | |
| Nov 21, 2017 at 0:29 | comment | added | Herman Tulleken | @IgorPak Indeed, very confusing! I am wondering if I understand what you are saying at all or are just completely out of my depth (I'm not a mathematician :-/ ) For example, wouldn't whatever "proves" there is an algorithm for a fixed set just be the algorithm for arbitrary sets? Or is it one of those things that exists without being exhibited explicitly? In any case, this comments are probably not the right medium for this; I will study the papers you linked (it will take some; I don't for example know what an "ideal" is from the top of my head.). One thing: is the manuscript still coming? | |
| Nov 20, 2017 at 4:58 | comment | added | Igor Pak | There is no formula. There is an algorithm for every fixed set of rectangles but not if the set of rectangles is an input. In fact, just because the algorithm exists for a given very large set of rectangles, does not mean it's computable. This is all confusing for a reason - the question is neither in Combinatorics nor Discrete Geometry but in Logic. Compare with the situation §7.2 of Jed Yang's paper arxiv.org/pdf/1212.3380.pdf | |
| Nov 20, 2017 at 3:57 | comment | added | Herman Tulleken | @IgorPak A formula would be ideal (in terms of $p_i$ and $q_i$), or a set of conditions (similar to Theorem 1), but failing that an algorithm would be good (especially if it is fast / does not require trying to find a tiling). Thanks for the link; I will give it a read. (Looks like the last part may allude to what I am asking for, without explicitly giving it.) | |
| Nov 20, 2017 at 1:47 | comment | added | Igor Pak | I don't understand what exactly is your question? Do you want a formula or an algorithm or what? About Lam-Miller-Pak paper. Much of it is written by Lam in this introductory note: math.lsa.umich.edu/~tfylam/HCMR/HCMR.pdf | |
| Nov 4, 2017 at 22:49 | history | edited | YCor |
edited tags
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| Nov 4, 2017 at 20:17 | answer | added | Herman Tulleken | timeline score: 4 | |
| Nov 2, 2017 at 20:55 | comment | added | Herman Tulleken | I was thinking of doing that next. | |
| Nov 2, 2017 at 15:57 | comment | added | Timothy Chow | Have you tried emailing Igor Pak or Thomas Lam? | |
| Nov 2, 2017 at 15:36 | comment | added | Herman Tulleken | @GerryMyerson Their paper deals mostly with proving things about simple tilings (like the number of rectangles that a simple tiling can have and the "average area" of rectangles in a simple tiling). Initially I thought that either (or both) simple tilings / fault-free tilings can be the "primitive" (and harder) problems, and that compound / faulty tilings can just be broken down into primitive problems. However, it seems the compound problems are inherently hard by themselves... | |
| Nov 2, 2017 at 15:32 | comment | added | Herman Tulleken | @AaronMeyerowitz It was late when I edited the post and I accidentally made the "correction" to Theorem 1. I fixed both now. I also added an additional condition that I left out; Theorem 3 only applies to sets of 3 or more rectangles. The area requirement is not mentioned in the Theorem in the source; I guess the other conditions make it true for rectangles with sides bigger than $C$. | |
| Nov 2, 2017 at 15:30 | history | edited | Herman Tulleken | CC BY-SA 3.0 |
Fixed Theorem 3 and undid earlier changes to Theorem 1
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| Nov 2, 2017 at 12:14 | comment | added | Gerry Myerson | Anything useful in Chung et al., Tiling rectangles with rectangles, math.ucsd.edu/~ronspubs/82_04_tiling.pdf ? | |
| Nov 2, 2017 at 4:53 | history | edited | Herman Tulleken | CC BY-SA 3.0 |
Fixed a mistake and added minor details.
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| Nov 2, 2017 at 4:34 | answer | added | Aaron Meyerowitz | timeline score: 6 | |
| Nov 2, 2017 at 1:42 | history | asked | Herman Tulleken | CC BY-SA 3.0 |