Timeline for Height growth for randomly falling Tetris like blocks ? What if Young diagrams are falling down?
Current License: CC BY-SA 3.0
8 events
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| Sep 11, 2017 at 21:28 | comment | added | R W | Concerning the sticky disks - I think the point is that the asymptotics are different. In the heap model the "width" is fixed and the height goes to infinity, whereas it seems that in order to exhibit the "sticky" behaviour the width and the height have to grow simultaneously. | |
| Sep 11, 2017 at 21:24 | comment | added | R W | Then you are in business - once again, the only difference is that you deal with pieces of height possibly greater than 1. The monoid language can, indeed, in principle deal with cancellations as well, but the current heap model has no cancellations. | |
| Sep 11, 2017 at 19:42 | comment | added | Alexander Chervov | No, no, you made no mistake -- my question, was about NON real Tetris - without cancellation, just it came to mind that monoid language can treat cancelation - just imposing some products to be identity ... | |
| Sep 10, 2017 at 21:38 | comment | added | R W | Oops - my bad - are you talking about the "real tetris" so that if a row is filled then it disappears? This feature is indeed missing in the heap theory. However, I still believe that the heap technique should be applicable here - with some modifications though. | |
| Sep 10, 2017 at 19:04 | comment | added | Alexander Chervov | @R W Thank you ! But still it is not quite clear why such interpretation is useful is there any result like those on famous "sticky disks" ? Or may be cancelation propert in Tetris can be related to product of elements equal to identity? | |
| Sep 8, 2017 at 20:26 | comment | added | R W | OK - so let me be more formal. You have a finite set $S$ (the bottom of tetris cylinder) and a finite collection of functions ("tetris pieces") $f:S\to\mathbb Z_+$. I presume that the pieces fall vertically, so that the horizontal translates of the same shape correspond to different functions above. The monoid operation consists in letting the pieces drop one by one until they reach the lowest possible position. Usually the "heap people" consider just 0,1 valued functions (pieces of height one linked horizontally) as pieces, but this assumption is not really necessary. | |
| Sep 8, 2017 at 19:05 | comment | added | Alexander Chervov | Thank you very much ! However it is not clear for me the relation of those monoids with Tetris like ... | |
| Aug 31, 2017 at 19:40 | history | answered | R W | CC BY-SA 3.0 |