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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.