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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 $(12^{m})^n$, 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 ZeroDiagonal Matrices
deleted 4 characters in body 
Sep 12 
answered  Symmetric ZeroDiagonal Matrices 
Sep 11 
revised 
Maximum possible number of similar threecolored triangles
added some explanations 
Sep 11 
answered  Maximum possible number of similar threecolored 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 