Dima Pasechnik
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 1d awarded Nice Answer 1d 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 well-defined set of generators of a (sub)ring - I'd have to check Derksen-Kemper 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 Calabi-Yau 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 $(n-1)!$ 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