Timeline for What is the number of equitriangulations of the n-cube?
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
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| Feb 17, 2015 at 20:11 | answer | added | Francisco Santos | timeline score: 3 | |
| Feb 17, 2015 at 13:20 | answer | added | Francisco Santos | timeline score: 4 | |
| Dec 15, 2014 at 8:49 | comment | added | Pietro Majer | Call a nice triangulation of $I^n$ special if, for any face f (of any dimension) of $I^n$, it induces a triangulation on f by simplices all having a common vertex. I think a question with some hope to be answered is, counting the number of these "special triangulations" of $I^n$ (see comments below David Eppstein's answer). | |
| Dec 15, 2014 at 7:58 | comment | added | Pietro Majer | @Włodzimierz, yes, I mean triangulations (though the OP is also interested in partitions). I wrote a comment below. | |
| Dec 15, 2014 at 7:51 | answer | added | David Eppstein | timeline score: 4 | |
| Dec 15, 2014 at 0:52 | comment | added | Włodzimierz Holsztyński | @PietroMajer -- triangulations or partitions? Please, if you really can, provide not 60 but just 5 nice triangulations of $\ \mathbb I^3$. (This should be easy for you, right)? | |
| Dec 14, 2014 at 22:50 | comment | added | Gjergji Zaimi | @DavidEppstein For the context in which this question came up, we were considering arbitrary partitions of the hypercube into simplices. However, both questions sound interesting. | |
| Dec 14, 2014 at 22:44 | comment | added | Pietro Majer | How many nice triangulations are there for $I^3$? I count $60$ of them. | |
| Dec 14, 2014 at 20:10 | comment | added | David Eppstein | By triangulation, do you mean that the simplices have to meet face-to-face, or just any partition of the hypercube into simplices? | |
| Dec 14, 2014 at 16:41 | comment | added | Pietro Majer | The volume of a simplex with integer vertices is an integer multiple of 1/n!, so a triangulation of the n cube is nice if and only if it is made by n! (non-degenerate) simplices. | |
| Dec 14, 2014 at 9:30 | comment | added | Per Alexandersson | Nice means "unimodular" in your case; you look for the number of unimodular triangulations. | |
| Dec 14, 2014 at 9:28 | answer | added | Włodzimierz Holsztyński | timeline score: -4 | |
| Dec 14, 2014 at 4:59 | comment | added | Gerhard Paseman | Do nice simplices have nice faces? Or are such simplices extra nice? It seems to me that the extra nice decompositions may admit an easier path to enumeration. Gerhard "Try Being Extra Nice Today" Paseman, 2014.12.13 | |
| Dec 14, 2014 at 3:27 | history | asked | Gjergji Zaimi | CC BY-SA 3.0 |