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location Moscow
age 36
visits member for 2 years, 10 months
seen Jul 19 at 6:55

Jun
24
comment When does a set of collinearity conditions imply collinearity of all of the points?
But what happens if all $n$ points should be distinct?
Jun
3
comment Covering fat objects with fat objects
"The slimness factor of a rectangle is identical to its aspect ratio" --- is this true? If you use a square rotated at $\pi/4$, you may cover an $a\times b$ rectangle by a square with side length $(a+b)/\sqrt2$...
May
29
comment A functional inequality
@Juanito: Are you sure then that there are no other misses? I am particularly interested in $t>1$ (in your present formulation, you don't say that $g(r^2)>g(r)^2$ --- is it what you wanted?).
May
28
answered A functional inequality
May
23
comment Is there a better proof of this fact in number theory/formal group theory?
Your `ideal' situation provides only $b_n\mid a_n$. Is it enough for you?
May
22
comment Quotients of the initial semiring
Recall that there are other homomorphic images of $\mathbb N$, namely the factors by a congruence $\sim_{a,b}$ defined as $x\sim_{a,b}y\iff x,y\geq a \;\wedge\; b\,\mid\,x-y$. A ring $\mathbb Z/n$ corresponds to $\sim_{0,n}$.
May
14
reviewed Reject suggested edit on nontrivial theorems with trivial proofs
May
7
comment “Japanese Theorem” on cyclic polygons: Higher-dimensional generalizations?
What about two decompositions into EQUAL number of simplices? Or (this is more likely to be true) into MINIMAL number of them?
May
6
comment Shortest supersequence of all permutations of $n$ elements
See oeis.org/A062714 (and links)...
May
6
comment Shortest supersequence of all permutations of $n$ elements
Here is length 12 sequence for $n=4$: 123412314231
Apr
14
comment Simple groups and words
At least, you should add that the word does not contain $n$th power of a word, where $n$ is the period of $S$; otherwise you may have words like $a^kb^na^{n-k}$ etc.
Apr
1
comment Square root of a complex matrix commuting with a given one
@GeoffRobinson: Oh yes, ypu are right. Sorry. I have added some words about this case; hopefully now they are correct;)...
Apr
1
revised Square root of a complex matrix commuting with a given one
Correction of the last (wrong) statement
Apr
1
revised Square root of a complex matrix commuting with a given one
deleted 1 characters in body
Apr
1
answered Square root of a complex matrix commuting with a given one
Mar
27
answered Symmetry on a sphere
Mar
26
answered What is the name for the type of matrices?
Mar
26
comment What is the name for the type of matrices?
You may regard $M_{a_1,\dots,a_{2^n}}$ as the `addition table' for $n$-dimensional vector space over $\mathbb F_2$.
Mar
3
comment About generalized Minkowski inequality
Recall that the Minkowski inequality turns into equality when $(x_1,\dots,x_n)$ and $(y_1,\dots,y_n)$ are proportional. Thus, if you perturb the function $x^p$ a bit in a neighborhood of some point $a$ (keeping monotonicity, convexity, whatnot) then you may set $a=x_n$ or $a=x_n+y_n$ refuting your inequality for the perturbed function.
Mar
2
comment Triangle with largest perimeter in a convex region
Sorry, my previous comment was a result of a miscomputation. The circle is indeed the best among ellipses.