# All Questions

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### Galois group of equation [on hold]

Let the equation $5x^6-12x^5-12x^4+204x^3+81x^2-792x+414=0$ The Galois group of $P(x)=5x^6-12x^5-12x^4+204x^3+81x^2-792x+414$ have solvable to be or not?
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### How to verify a vector has a steady gradual increase mathematically? [on hold]

I rank the values inside my vector then look to verify the values have a gradual but steady increase. Ideally if I had 10 numbers the smallest would occur first and the second smallest would rank ...
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### Hyperbolicity of Deligne-Mumford stacks

Let $X$ be a smooth finite type separated connected Deligne-Mumford stack over $\mathbb C$ (with trivial generic stabilizer if necessary). This question is about "hyperbolicity" and it is motivated ...
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### Does every smooth, projective morphism to $\mathbb{C}P^1$ admit a section?

Possibly this has already been asked, but it came up again in this question of Daniel Litt. Does every smooth, projective morphism $f:Y\to \mathbb{C}P^1$ admit a section, i.e., a morphism ...
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### Characterize the category of rings

(Sub)categories of many well-studied mathematical objects have been characterized purely in terms of their morphisms. Some (famous) examples: Sets and functions, due to Lawvere. Modules over some ...
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### Find the integral [on hold]

How can we find the integral of the 1/(1+x^4) in the interval -infinity to +infinity.I tried to find and got it to be pi/sqrt(2). Am I correct? Please help me with an appropriate method. I tried to ...
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### When are all sums of the elements of a set different?

Consider a set $S = \{x_1, \dots, x_n\} \subset \mathbb{Q}\setminus\{0\}$ and assume that for any $I, J \subset [n]$ with $I \neq J$ we have that \sum_{i \in I} x_i \neq \sum_{j \in ...
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### Recognizing bridgeless cubic graph with special 2-factor

A 2-factor of graph $G(V, E)$ is a set of vertex-disjoint cycles that cover $V$. It is known that every connected bridgeless cubic graph contains a 2-factor (and a perfect matching). I conjecture ...
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### Painting $n$ balls from $2n$ balls red, and guessing which ball is red, game

The game Lucy has $2n$ distinct white colored balls numbered $1$ through $2n$. Lucy picks $n$ different balls in any way Lucy likes, and paint them red. Lucy then giftwrap all the balls so that it is ...
### Does Schur's Lemma hold in this case? Regular representations of $S_n$ over $\mathbb R$
Warning I am a physicist and I am not familiar with a lot of the machinary of representation theory. I consider the regular representation of $\mathbb S_n$ over reals $\mathbb R$ (\$\mathbb R \mathbb ...