Timeline for Meaning of "combinatorial data"
Current License: CC BY-SA 4.0
11 events
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| Jul 12, 2020 at 4:50 | history | edited | user267839 | CC BY-SA 4.0 |
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| Jul 11, 2020 at 23:12 | history | edited | user267839 | CC BY-SA 4.0 |
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| Jul 11, 2020 at 23:06 | history | edited | user267839 | CC BY-SA 4.0 |
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| Jul 11, 2020 at 22:57 | comment | added | user267839 | Therefore not every subset of the power set $P(V)$ of $V$ is a abstract simplicial complex. So to determine which subsets of $P(V)$ can occure as abstract simplicial complexes is a combinatorial problem. But how to draw the same analogy to cech cycles isn't clear to me. Is it possible to associate abstractly a abstract simplicial complex to a Cech cycle in order to "make" it combinatorial? | |
| Jul 11, 2020 at 22:57 | answer | added | paul garrett | timeline score: 2 | |
| Jul 11, 2020 at 22:42 | comment | added | user267839 | yes I thought that orginally this arose from the concept of abstract simplicial complex: a data $S$ consisting of vetrices $V={v_1,v_2,...,v_n}$ an a $m$-simplex of $S$ is a subset ${v_{i_1},..., v_{i_m}}$ of $V$. $S$ is called abstract simplicial complex if for every $m$-simplex ${v_{i_1},..., v_{i_m}}$ contained in $K$ every subset ${v_{i_{j_1}},..., v_{i_{j_d}}}$ is (as a $d$-simplex) is contained in $S$. | |
| Jul 11, 2020 at 21:58 | history | edited | YCor | CC BY-SA 4.0 |
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| Jul 11, 2020 at 21:40 | history | edited | Carlo Beenakker | CC BY-SA 4.0 |
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| Jul 11, 2020 at 21:38 | comment | added | Carlo Beenakker | the origin of the name as well as a general definition is discussed in Wikipedia --- the combinatorial map tells you how to combine simplices to form a simplicial complex. | |
| Jul 11, 2020 at 21:35 | comment | added | Gro-Tsen | I don't think there's a precise formal meaning. I understand it to mean something Kronecker would approve of, i.e., an essentially finistic mathematical object, something you could encode on a computer (e.g., a finite graph or hypergraph, as opposed to something like a differentiable manifold). | |
| Jul 11, 2020 at 21:26 | history | asked | user267839 | CC BY-SA 4.0 |