Timeline for What rectangles can a set of rectangles tile?
Current License: CC BY-SA 4.0
7 events
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| Dec 24, 2022 at 8:43 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
http -> https (the question was bumped anyway)
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| Nov 2, 2017 at 7:03 | history | edited | Aaron Meyerowitz | CC BY-SA 3.0 |
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| Nov 2, 2017 at 6:58 | history | edited | Aaron Meyerowitz | CC BY-SA 3.0 |
added 853 characters in body
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| Nov 2, 2017 at 6:30 | comment | added | Herman Tulleken | Interestingly, I noticed now (looking for 3 rectangles with co-prime sides) that all the tilings I found so far (for $m, n < 75$) each always has at least 1 side with a factor of either 6, 10, 15; and if one side is prime, the other is a multiple of 30. I wonder if some stronger version of Theorem 2 is true (which will mean we cannot find a $C$...) (Also, it would be disappointing if the only known algorithm that realizes Theorem 4 is the one you mentioned... because the smaller cases take verrrrry long to enumerate.) | |
| Nov 2, 2017 at 6:10 | comment | added | Aaron Meyerowitz | I should have realized about theorem $3$! I thought the techniques in the two papers might about answer your question about theorem 4. The fact that the time is essentially that of reading the rectangle dimensions makes me think that in finite pre-processing time a criterion can be found that then makes the decision problem almost immediate. | |
| Nov 2, 2017 at 5:09 | comment | added | Herman Tulleken | Your answer made me realize I made a mistake in typing up Theorem 3 (which I now corrected). This means your suggestion does not work directly (see Theorem 2), but the idea may still work (by finding 3 rectangles tileable which satisfy the conditions). I am also aware of the two papers you linked; however, on first reading it seemed not to offer anything more than what is in Theorem 3 (at least for 2D, for higher dimensions it looks like their method makes the more complicated conditions easier to handle). But I will have another look, thanks! | |
| Nov 2, 2017 at 4:34 | history | answered | Aaron Meyerowitz | CC BY-SA 3.0 |