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May
20
reviewed Reject suggested edit on nontrivial theorems with trivial proofs
May
20
comment doubly-stochastic isomorphisms of graphs
Actually, the same argument can be carried out for $A$ being the adjacency matrix of Petersen, with the obvious changes.
May
20
comment doubly-stochastic isomorphisms of graphs
I denote by $A$ the complement of Petersen's adjacency matrix
May
20
comment doubly-stochastic isomorphisms of graphs
In the paper I cite they proved that the complement to Petersen is not compact, and derive the non-compactness of the Petersen itself from it.
May
20
answered doubly-stochastic isomorphisms of graphs
May
20
comment doubly-stochastic isomorphisms of graphs
Is Petersen the smallest example? I guess it is small enough to attempt a computer enumeration of vertices of such a polytope. Has anyone tried this?
May
15
comment Is there an Ehrhart polynomial for Gaussian integers
Yeah, right, I didn't think straight. Sorry for noise.
May
14
comment Integrally closed polytopes from 01-matrices
Isn't every $p\in kP$ by definition equal to $p=q+...+q$, for $q\in P$? Or do you mean to have $p_i\neq p_j$ for $i\neq j$ ?
May
14
comment $xyz = \frac{7}{16}\left(\frac{2x - y - z}{3}\right)^3$ in nonvanishing integers
probably working in Sage will give you more info. It can identify the curve in certain database, etc...
May
14
answered Approaches to implicitly defining generating function
May
14
comment Approaches to implicitly defining generating function
(continuing) let $F$ be the GF for a recursively enumerable language with non-recursively enumerable complement, and $A$ the GF for the language of all words. Then $A-F$ is the GF for the complement of $F$, i.e. for a non-Chomsky language.
May
14
comment Approaches to implicitly defining generating function
If it is the way I described in my comment then there certainly are GFs not corresponding to any language in Chomsky hierarchy, as the latter must be recursively enumerable, a property known not to be closed under taking the complement.
May
14
comment Approaches to implicitly defining generating function
I am not sure if it is well-known how does a language $L$ correspond to a generating function $F(t)=\sum_i a_i t^i$. Is $a_i$ equal to the number of length $i$ words in $L$?
May
13
comment Is there an Ehrhart polynomial for Gaussian integers
naively, at least if $|a+ib|\in\mathbb{Z}$, this should follow from the classical case; indeed, by multiplying by $a+ib$ you apply to your $\mathbb{C}$-plane the composition of a rotation and the scalar matrix $C=|a+ib|I$, and so the integer points would behave in the same way as by scaling with $C$ alone.
May
13
answered adjacency matrix of a graph and lines on quartic surfaces
May
12
comment Is there an Ehrhart polynomial for Gaussian integers
I was under impression that the quasiperiodicity of Ehrhart polynomial holds for any lattice $\Lambda$ in $\mathbb{R}^d$ and a polytope with vertices in $\Lambda$. How does your setting differ?
May
7
comment Limit of a hypergeometric integral
could you perhaps try using an integral representation of $ _2F_1$ and swap limits of integration (assuming this is legal to do)?
Apr
24
revised Diagonalization for sums of Hermitian matrices
english corrections
Apr
13
comment Fast checking that overdetermined polynomial system does not have a solution
Note that the 1st method is not exact, and the software mentioned does its work with the usual floating point numbers. Particularly if your integer coefficients will get long, this won't be very reliable. That is to say, that you will have to look inside your systems just to make sure the coefficients don't blow up.
Apr
4
comment Does a spherical building embeds in a building of type $A_n$?
well, I won't be surprised if this has been improved (perhaps even by Tits himself) - that's why I referred to the book that is more or less the state of the art.