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If it turns out that a problem is equivalent to a known open problem, then the open-problem tag is added. After that, the question essentially becomes, "What is known about this problem? What are some possible ways to approach this problem? What are some ways that people have tried to attack it before, and with what results?"
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Irreducible polynomials with constrained coefficients
Over at the Cafe, after reading about TWF 285, I asked more-or-less
About how many polynomials with coefficients in $\{\pm 1\}$ and of degree $d$ are irreducible?
and that's what I want to ask …
-1
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When shorter means smaller?
Another tact; consider the set of foldings of our convex shape. Since the fold axis partitions the perimeter into two parts, and by convexity both have finite length, so one of them is at least half …
1
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When shorter means smaller?
An incomplete answer; but perhaps it helps to rephrase the problem as below. The reason the round circle does have this property is that without loss of generality, the map $f$ fixes the origin; and …