Ilya Bogdanov
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 6h comment When is $a^{2^n}+1$ prime finitely often unconditionally? OK, I see, there is a great difference between "can be prime finite number of times" and "cannot be prime infinite number of times"... 1d comment Consecutive numbers with three numbers using the measure of an Isoceles triangle But what is the question? 1d comment non commutative polynomial which is zero for all matrix evaluation Still, the Amitsur--Levitski theorem provides the minimal degree of such polynomial for a fixed $m$, and this degree is $2m$. So it provides the answer for the original question. 1d comment Weighted maximal number of disjoint chains in the integer divisibility poset for $\{1,2,\ldots,n\}$ The set up is not clear for me, sorry. Are $y_1,y_2,\dots$ fixed numbers? If yes --- are they chosen so that $C_x\cap C_{x'}=\varnothing$, or it is our constraint to choose $x_1,x_2,\dots$ so that the resulting sets are disjoint? Nov 25 reviewed Close Modifying tensor to be positive definite everywhere Nov 23 comment Unit in cyclotomic field We have $1+2(\zeta+\zeta^{-1})=\frac2\zeta(\zeta-a)(\zeta-\bar a)$, where $a=(-1+i\sqrt{15})/4$ (notice that $|a|=1$, and $2a$ is an algebraic integer). Thus the norm is 1 iff $2^{\varphi(n)/2}|\Phi_n(a)|=1$. At least, this should mean that some $n$th root of unity is sufficiently close to $a$... Nov 20 answered Do graphs with $\omega(G) = \chi(G)$ grow “common” as $|V|$ grows large? Nov 20 comment A point set of power series with coefficients in {-1, 1}. Connected or not? Take $|z|=1/3$. If $a_1=1$, then the corresponding element of $X_z$ is at distance of $\leq 1/6$ from $z$, otherwise it is at distance of $\leq 1/6$ from $-z$. Thus $X_z$ is disconnected. A more interesting question arises when $|z|>1/2$ (and now it may depend on the argument of $z$ as well)... Nov 19 comment Volume growth of balls II Hm. On the definition: Am I right that the left limit is always $\leq 1$, while the right one is always $\geq 1$, so both should equal 1? Nov 18 reviewed Close Generalized Sphere Kissing Problem Nov 18 reviewed Close What the number of the components of a specific subgraph? Nov 18 reviewed Reviewed Coefficients of Ehrhart polynomials, in the binomial-coefficient basis Nov 12 answered A question about a specific partition of a graph Nov 8 answered Isomorphic Hadwiger graphs Oct 30 comment Kernel of skew-symmetric matrix of rank $n-1$ with $n$ odd: is this a known result? $\overline M_{\hat1\hat j}$ is an $(n-1)\times (n-1)$ matrix obtained by removing two rows and two columns. See en.wikipedia.org/wiki/Pfaffian#Recursive_definition Oct 26 answered Existence of an infinite word with a predetermined asymptotic for the word complexity Oct 26 comment How to show it is contained in a convex hull? 1) The claim is sharper, since $\mathop{\rm conv}(S-F_i)$ becomes smaller in this case. 2) The condition of non-intersection was used in the middle: all vertices of $\mathop{\rm conv} S$ belonging to $F_i$ form a connected (by edges) set, so there exists an edge with the vertices of the same color. In turn, this condition is needed to establish that the simplex to be cut is not polychromatic. Oct 25 answered How to show it is contained in a convex hull? Oct 25 comment How to show it is contained in a convex hull? What does $\mathcal H(\cdot)$ denote? Oct 25 reviewed Close A question from Hilbert's Nullstellensatz