Timeline for "Pythagoras number" for integral matrices
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 14, 2015 at 7:46 | comment | added | Hans | okay, many thanks! I'll have to read these works. | |
| Oct 14, 2015 at 6:27 | comment | added | few_reps | Right ! Strangely, the review of this paper doesn't speak about Icaza's result, hence did not appear when I tried with "Icaza" in the field "anywhere" ! Their result says that $g(n)=O(3^{\frac n2}\log(n))$ which is quite better than Icaza's bound. | |
| Oct 14, 2015 at 6:03 | comment | added | WKC | Kim and Oh (2005?) give an explicit upper bound for $g(n)$ for all sufficiently large $n$, which is more or less exponential in $n$. | |
| Oct 14, 2015 at 5:43 | comment | added | few_reps | After looking at mathscinet notices (not at the papers themselves), Icaza's result seems to be the only general theorem ... the bound she obtains has the form $g(n)\leq 8+\sum_{k=1}^n c_k$ where $c_k$ is the (highly explosive) number of isometry classes of $k$-dim. unimodular lattices. All other results seem to find better bounds for small values of $n$. | |
| Oct 14, 2015 at 5:33 | comment | added | WKC | @few_reps Yes, you are right. Thanks. | |
| Oct 14, 2015 at 5:32 | history | edited | WKC | CC BY-SA 3.0 |
added 12 characters in body
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| Oct 14, 2015 at 5:30 | comment | added | few_reps | In the first paragraph you mean $S(n)$ is the set of $n$-dimensional lattices that are represented by some euclidean $\mathbf Z^m$ (and the result is that there exists $g(n)$ such that any element of $S(n)$ is represented by the euclidean $\mathbf Z^{g(n)}$, right ? | |
| Oct 14, 2015 at 5:08 | history | answered | WKC | CC BY-SA 3.0 |