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Apr
20
comment Why polynomial $\psi^\top(t) A^{-1} \psi(t)$ attains maximum on $[-1, 1]$ at $t = \pm 1$, where $\psi_k(t) = t^k$?
Then it is better to correct the mess your question...
Apr
19
revised Why polynomial $\psi^\top(t) A^{-1} \psi(t)$ attains maximum on $[-1, 1]$ at $t = \pm 1$, where $\psi_k(t) = t^k$?
added 27 characters in body
Apr
18
revised Why polynomial $\psi^\top(t) A^{-1} \psi(t)$ attains maximum on $[-1, 1]$ at $t = \pm 1$, where $\psi_k(t) = t^k$?
added 19 characters in body
Apr
18
answered Why polynomial $\psi^\top(t) A^{-1} \psi(t)$ attains maximum on $[-1, 1]$ at $t = \pm 1$, where $\psi_k(t) = t^k$?
Apr
18
comment What are the central points of a semi-nice region in the plane?
How would you find the central point of an annulus?
Apr
18
comment Bases of the special form
Surely - I've edited the indices. As for he second question: that was another typo, I meant $V_2'=V_2$, since both equal $\langle \beta_0,h^{-1}\beta_0\rangle$...
Apr
18
revised Bases of the special form
edited body
Apr
18
answered Bases of the special form
Apr
15
comment The properties of Pos
Which type of convergence do you mean? If it is "pointwise", then, as $n\to\infty$, the first $k$ terms of $X_1(\omega)$, $X_2(\omega)$, $\dots $ are whp disinct for any fixed $k$, so $Pos(Pos(f_n))|{[1,k]}$ whp coincides with $\mathord{id}_{[1,k]}$. I assume you mean something different?
Apr
8
revised Set of balls which the number of the ball intersects lines on the plane is bounded
added 5 characters in body
Apr
8
comment Reference request: exponential growth rates of subword-closed languages are integers
The claim about finiteness of the set of minimal words not in $L$ looks strange. Do you need exponential growth to state it? Otherwise it is false, as the language $\{a^kb^\ell a^m\colon k,\ell,m\geq 0\}$ shows. The minimal words not in $L$ are $ba^{k+1}b$ for all $k\geq 0$.
Apr
7
reviewed Leave Open Maximum size of minimal sequence of transpositions whose product is a given permutation
Apr
7
comment Maximum size of minimal sequence of transpositions whose product is a given permutation
Why don't you apply the next transpositions to green permutations? As far as I understand, the subsequence does not need to consist of consecutive terms of the initial sequence. Also, $n\log n$ surely is not achievable, because you cannot reverse the order by using $(i,i+1)$ in less than $n\choose 2$ steps, due to the number of inversions changing by 1 at each step.
Apr
6
comment Generic set that is a proper subgroup
On the additional question: surely yes. Let $G$ be the free group with $N$ generators, and let $H$ to be the subgroup of all irreducible words of even length.
Apr
5
comment Tricky two-dimensional recurrence relation
@მამუკა ჯიბლაძე: Surely! Also, my arguments can be rewritten in the language of generating functions as well.
Apr
5
awarded  nt.number-theory
Apr
4
answered Sturmian subword whose reverse is not a subword
Apr
4
answered Tricky two-dimensional recurrence relation
Apr
4
awarded  Civic Duty
Apr
4
comment Partitioning finite directed graphs into 3 “incoming-sparse” sets
I do not say your example is wrong; just the reasoning looks strange. Also, the example on 7 vertices does not work (for the new formulation)...