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20h
comment Strictly positive solutions of a random linear system
Oh yes, surely $m$ instead of $n$. @alex: if $x_k$'s are small enough then $x_{j_i}$ is $c_i$ decreased by a small number, hence it is positive.
20h
revised Strictly positive solutions of a random linear system
edited body
1d
comment Decomposition of symmetric homogeneous polynomials
Still, for $x^2+y^2+x+y$ it is impossible: $x$ and $y$ cannot appear in neither of your summands since all of them are homogeneous of degree $2$.
1d
comment Strictly positive solutions of a random linear system
I have added some words on the uniform bound (i.e. the one working for all admissible $c$). If it is not what you want, you need to specify the set of valid $c$ (it should depend on $m$...).
1d
revised Strictly positive solutions of a random linear system
a lower bound added
1d
comment Strictly positive solutions of a random linear system
The probability of ONE bad event is $(1-2^{-m})^n$, and you have $n$ possible bad events. The probability of their union does not exceed the sum of their probabilities. What's wrong?
1d
answered Strictly positive solutions of a random linear system
1d
answered Monotonicity of the gap of permutated sequence
Sep
12
revised Symmetric Zero-Diagonal Matrices
deleted 4 characters in body
Sep
12
answered Symmetric Zero-Diagonal Matrices
Sep
11
revised Maximum possible number of similar three-colored triangles
added some explanations
Sep
11
answered Maximum possible number of similar three-colored triangles
Sep
9
answered Fractional Part Problem
Sep
4
awarded  Yearling
Sep
3
comment A functional inequality
Yes you can, but I do not think it was quite essential...
Aug
12
awarded  Nice Answer
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