Nov
19 |
comment |
Is there a similar theory as for symmetric polynomials, that deals with polynomials on the entries of matrices that are symmetric in both dimensions?
I mean Pouzet conjectured that some statement A about invariant rings implies B which is the graph satisfies the graph isomorphism property, i.e., it is the only one up to isomorphism with the same unordered list with repetition of subgraphs with one less vertex. Now Thiery proved that (A implies B) is false. So my question is what remains of the "sound" "general setup"? Are there precise viable substitutes for Pouzet's conjecture written somewhere in the literature? |
Nov
19 |
comment |
Is there a similar theory as for symmetric polynomials, that deals with polynomials on the entries of matrices that are symmetric in both dimensions?
@Dima: thanks but when I checked my copy of Dersken-Kemper what they say about the connection graph isomorphism pbm<->invariant rings does not sound good. Pouzet's conjecture to this effect was shown to be false by Thiery. So is there still a precise viable connection in the literature? |
Nov
17 |
awarded | Nice Answer |
Nov
12 |
comment |
Is there a similar theory as for symmetric polynomials, that deals with polynomials on the entries of matrices that are symmetric in both dimensions?
@Dima: what you said about bipartite graphs sounded very interesting, but did not have enough details for me to understand it well. What specific problem from the theory of bipartite graphs could one solve if one had a good enough description of the invariant ring that the OP is asking about? References would be appreciated. |
Nov
12 |
answered | Is there a similar theory as for symmetric polynomials, that deals with polynomials on the entries of matrices that are symmetric in both dimensions? |
Nov
11 |
answered | Can a general binary sextic form be put into the following form? |
Nov
11 |
comment |
Involutions of binary sextic forms
My paper with Chipalkatti refers to my co-author's article on the degree 18 of the binary quintic, not sextic. The latter is due to Hermite. I actually don't know who first discovered the degree 15 invariant for sextics. What kind of info would you like on this degree 15 invariant? |
Sep
22 |
comment |
Name for an orthogonal decomposition of $L^2 (\mathbb{R}^2; \mathbb{C})$
yes. I always wondered also about combinatoric vs combinatorial... |
Sep
22 |
answered | Name for an orthogonal decomposition of $L^2 (\mathbb{R}^2; \mathbb{C})$ |
Sep
22 |
comment |
The Guinand-Weil explicit formula without entire function theory
another very nice introductory reference for the explicit formula is the article "The explicit formula in simple terms" by Jean-Francois Burnol available here arxiv.org/abs/math/9810169 |
Sep
18 |
awarded | Nice Answer |
Sep
14 |
comment |
Wavelet-like Schauder basis for standard spaces of test functions?
@Pedro: indeed othogonality would have to be sacrificed. Thanks for pointing out the LP wavelets from Meyer's book. I will have a look. |
Sep
11 |
comment |
Examples of major theorems with very hard proofs that have NOT dramatically improved over time
I don't know if it is simpler but there seems to be a more "conceptual" proof arxiv.org/abs/1305.0926 by Maculan which relates the result to GIT and Arakelov geometry. |
Sep
11 |
answered | Examples of major theorems with very hard proofs that have NOT dramatically improved over time |
Sep
10 |
comment |
Uniform definition of $S(\mathbb{R})$ and $S(\mathbb{Q}_p)$
other issue with "subspace of $L^1\cap L^2$, Fourier stable, dense and nuclear": nuclearity with respect to which topology? |
Sep
10 |
comment |
Uniform definition of $S(\mathbb{R})$ and $S(\mathbb{Q}_p)$
by nuclear you mean the more general definition of Grothendieck rather than countably Hilbert, right? |
Sep
10 |
comment |
Wavelet-like Schauder basis for standard spaces of test functions?
Thanks Paul. I am familiar with this Schauder basis and I do use it a lot in my research interests. Unfortunately, it is not wavelet-like. It is not good for the kind of microlocal harmonic analysis I would like to do. |
Sep
10 |
comment |
Uniform definition of $S(\mathbb{R})$ and $S(\mathbb{Q}_p)$
my motivation comes from probability theory on the duals of these spaces. In the p-adic case I really want S' where S is the locally constant space not the one with rapid decay of f and its Fourier transform. |
Sep
10 |
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Uniform definition of $S(\mathbb{R})$ and $S(\mathbb{Q}_p)$
I know, but what I am saying is if the expression "locally constant" occurs at all in the definition then I don't find the latter satisfactory. This sounds especially strange in the real special case since the requirement is vacuous for lack of locally constant functions. |
Sep
10 |
revised |
Uniform definition of $S(\mathbb{R})$ and $S(\mathbb{Q}_p)$
edited tags |