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awarded  Nice Answer 
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awarded  Yearling 
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?
@AbdelmalekAbdesselam : the general setup is that if you have a system of parameters $P$ (or some other welldefined set of generators of a (sub)ring  I'd have to check DerksenKemper to see exactly which one) of the corresponding invariant ring, and evaluate your graph (as a vector of 0s and 1s) on this system, you will get a unique fingerprint, distinguishing nonisomorphic graphs. Pouzet's conjecture was that certain set $P'$ is generating the same ring as $P$, but this turned out to be false. 
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?
@AbdelmalekAbdesselam : what do you mean by "doesn't sound good"? That they make an error? IIRC, these conjectures were about particular generating sets for rings, not about general setup. The latter is sound, I think. 
Nov
13 
revised 
How to calculate log or exp of a value in GF(2^n) using log/exp table of GF((2^k)^m) where n=k*m?
TeXify and fix some English... 
Nov
13 
revised 
Proving Richardson's theorem for constants
tag added 
Nov
13 
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?
it's known how to search for generators for invariant rings of permutation groups, of which we have an example here (e.g. take orbit sums of monomials, up to certain degree). The problem is that such a set will be huge, and will have huge degrees. 
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?
@AbdelmalekAbdesselam : having a "good" set of generators for such a ring (or only a system of parameters for such a ring) would allow one to solve the isomorphism problem for bipartite graphs (which is as hard as for general graphs  cf. e.g. en.wikipedia.org/wiki/…). How a similar idea works for general graphs, is explained in the book I cited in the answer. 
Nov
12 
reviewed  Approve Line bundles with vanishing cohomology on CalabiYau manifold 
Nov
11 
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 
revised 
Recurrence sequence
tex fix 
Nov
8 
awarded  Autobiographer 
Nov
6 
awarded  Popular Question 
Nov
6 
revised 
do you know this determinant (basic commutative algebra)?
removed no longer working typesetting workarounds like < instead of < 
Nov
3 
comment 
What does Kqn means here?
just a typo, perhaps? 
Oct
27 
comment 
Weights on cyclic orderings
we (and Woodall, and Kleitman) define the graph on these $(n1)!$ elements of $S_n$, so that two such elements are adjacent if one needs to swap two adjacent positions to get one from the other. 
Oct
27 
comment 
How to find solutions for four polynomial equations with four unknown variables using Resultant Theory
you should also specify whether you look for complex solutions, or only for real solutions, or actually it happens over some other field... 
Oct
26 
answered  Weights on cyclic orderings 
Oct
26 
comment 
Strongly connected graph and the eigenvalues of the laplacian matrix
so you see, the laplacian has one eigenvalue 0, and 2 conjugate complex eignevalues, each with multiplicity 3. 
Oct
26 
comment 
Strongly connected graph and the eigenvalues of the laplacian matrix
sure, see the edited answer 