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Apr
28
comment Does it make sense to compare sets (polytopes) with different dimensions?
@QiaochuYuan - the OP means to say that a linear program $X$ gives better optimum than a linear program $Y$, and denotes this fact by $X\subseteq Y$. I already complained in my 1st comment that it's a very misleading notation.
Apr
28
comment Does it make sense to compare sets (polytopes) with different dimensions?
@QiaochuYuan - here $\subseteq$ meant to compare quality of models, rather than anything else...
Apr
28
comment Does it make sense to compare sets (polytopes) with different dimensions?
it's very confusing to use containment, i.e. $\subseteq$ relation, to describe your setting. Polytopes are just sets, and $A\subseteq B$ would be read as containment of sets...
Apr
22
comment Eigenvalues of partial Hankel matrices
what is "partial" about your matrices?
Apr
20
comment Complexity of solving systems of linear diophantine equations
I edited the answer to indicate what you say; indeed, it's not as clear.
Apr
20
comment Complexity of solving systems of linear diophantine equations
how to compute the transformation (with a slightly worse complexity) is shown in "Asymptotically fast computation of Hermite normal forms of integer matrices" by Storjohann and Labahn: dx.doi.org/10.1145/236869.237083
Apr
20
comment Finite groups generated by 3 involutions interchanging disjoint residue classes of the integers
It's a quotient of a Coxeter group with 3 generators, in each case, right? Could you specify the order of the product of each pair of generators?
Apr
20
comment Complexity of solving systems of linear diophantine equations
see my answer. still, AFAIK, the transformations needed are explicit.
Apr
20
comment Complexity of solving systems of linear diophantine equations
IIRC, the transformation matrices can be trivially recovered, as they basically trace the steps taken by the SNF computation.
Apr
20
comment Complexity of solving systems of linear diophantine equations
OK - by the way, have a look at sciencedirect.com/science/article/pii/S0024379598100125
Apr
20
comment Complexity of solving systems of linear diophantine equations
I think you should be more specific regarding what you mean by "solved". E.g. one may think of $b=0$ and $x$ being an infinite set (so no finite time, leave alone polynomial), or a basis of a $\mathbb{Z}$-lattice, or yet something else...
Apr
19
comment Intuition about Toroidal Embeddings
It would be great if there was an example of some "really non-convex" polyhedron, e.g. a triangulation of a torus in $\mathbb{R}^3$ corresponding to some explicit variety...
Apr
17
comment Dao's theorem on six circumcenters associated with a cyclic hexagon
@OaiThanhĐào : one never says "I thank to you..."; it's just "Thank you...".
Apr
12
comment Torsion-free, normal subgroups of certain Coxeter groups
it depends; if I recall correctly, $\sqrt{2}$ appears when you work with crystallographic groups. You will find all the details in the book I cited, or in one of their papers. Here is another work of this kind : sciencedirect.com/science/article/pii/S019688580400003X
Apr
12
comment Gramian of a permutation group orbit
think of the case $k=1$. Surely $W$ need not have any symmetry in it at all.
Apr
12
comment Chasing a 1950s thesis from the University of Dhaka on block designs
looks like a typo in the title; it should be "...DesignS".
Apr
5
comment If the two smallest eigenvalues of the Laplacian matrix of a network are equal to zero, then does it mean that the network is not connected?
the multiplicity of the 0 eigenvalue is the number of connected components.
Apr
5
comment Cayley graphs of $A_n.$
Benjamin's answer does prove it.
Mar
31
comment Positive definite - Inverse of sparse symmetric matrix
do you need $P^{-1}$ to be sparse? Otherwise it is trivial...
Mar
28
comment How I can prove the equality $P^{P_{\operatorname{space}}}=NP^{P_{\operatorname{space}}}=P_{\operatorname{space}}^{P_{\operatorname{space}}}$
I am not saying that complexity theory questions have no place here, I am saying that this particular one is way too technical to be of interest here.