Timeline for volume over a hypercube, over simplex: twist by Euler numbers
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| May 3, 2017 at 20:07 | comment | added | Ira Gessel | A reference for Fedor Petrov's comment is Richard P. Stanley, Two poset polytopes, Discrete Comput. Geom. 1 (1986), no. 1, 9–23, dedekind.mit.edu/~rstan/pubs/pubfiles/66.pdf. | |
| May 2, 2017 at 11:55 | comment | added | T. Amdeberhan | @ZurabSilagadze: This is cool. I wish we can give a direct transformation rule from $\square$ to $\Delta$ shapes, because your idea goes through $\square$ to $\delta$ and then followed by algebraic comparison of the volumes of $\Delta$ and $\delta$. | |
| May 2, 2017 at 10:44 | comment | added | Zurab Silagadze | Yes, indeed if we mean the volume of the zigzag chain polytope (see, for example arxiv.org/abs/0912.4240). However, $\delta_n$ is not quite a zigzag chain polytope because of $n_n+u_1\le 1$ extra condition. | |
| May 2, 2017 at 10:36 | history | edited | Zurab Silagadze | CC BY-SA 3.0 |
Some extra text added
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| May 2, 2017 at 5:27 | comment | added | Fedor Petrov | It is well known that the volume of $\{u_i\geq 0, u_i+u_{i+1}\leqslant 1\}$ equals Euler number divided by factorial. Though I can not give a reference immediately. | |
| May 2, 2017 at 5:23 | history | edited | Zurab Silagadze | CC BY-SA 3.0 |
typos corrected
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| May 2, 2017 at 5:17 | history | edited | Zurab Silagadze | CC BY-SA 3.0 |
some corrections
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| May 2, 2017 at 5:09 | history | answered | Zurab Silagadze | CC BY-SA 3.0 |