# All Questions

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### Polynomials with few prime factors

It is a long standing problem to investigate whether irreducible integral polynomials not divisible by a fixed square integer assumes square-free values infinitely often. The result is known ...
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### Does the smooth manifold $\#_{l}CP^{2}\#_{k}(-CP^{2})$ admit a symplectic structure?

Let $-CP^{2}$ denote the complex projective surface $CP^{2}$ with the reverse orientation. I have seen some results about the existence of symplectic structures on the connected sums ...
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### Number of inclusive relations on an n-set [on hold]

A binary relation on a set T is inclusive if every element in T relates to at least one element. Find the number of inclusive relations on an n-set for n = 1, 2, 3 and for arbitrary n.
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### Supremum in a markov chain model

A markov chain $X$ with finite state space $\{1,2,\cdots,N\}$ is defined on a probability space $(\Omega, P, \mathcal{F})$ equiped with filtration $\{\mathcal{F}_t\}$. And we assume that we can reach ...
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### Relationship of height zero hypercovers to co-cartesian condition on cosimplicial modules

Suppose given a cosimplicial ring $R^\bullet$ and a cosimplicial module $M^\bullet$ (i.e. a cosimplicial Abelian group such that $M^n$ is an $R^n$-(left/right/bi)module). I have seen it said that ...
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### Are There Always Group Generators Which Give Unimodal Growth

Suppose G is a k-generated finite group. Is there always a set of k elements which generate the group and have a unimodal counting function? Background: The counting function, f(n), is a function ...
2answers
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### Behavior of duality under pull-back

I have a technical question on commutative algebra. I am not an expert in the subject, and I would like to know if there are "typical conditions" making the following possible. Let $\varphi:R\to S$ ...
0answers
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### spherical map of fixed points?

Let $B = \{\, x \in \Re^m : \|x\| \le 2 \,\}$, and let $f : B \to B$ be a continuous function whose set of fixed points is $S^k = \{\, x \in B : \|x\| = 1, x_{k+2} = \cdots = x_m = 0 \,\}$. Can it ...
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### Finer motivic decomposition in a bigger motivic category

In http://www.youscribe.com/catalogue/rapports-et-theses/savoirs/motives-of-projective-homogeneous-varieties-elektronische-ressource-1433377 Semenov shows that the Motivic decomposition of a variety ...
1answer
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### Generalizations of Chen's theorem

The two famous theorems of Jingrun Chen, both with similar proofs, state (respectively) that all sufficiently large even numbers are the sum of a prime and an element of $P_2$, and that there are ...
0answers
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### Certain subgroup of automorphism groups of binary codes

Suppose that $C$ is an binary linear code of length $n$ and dimension $k$ (i.e. it's a $k$-dimensional linear subspace of $\mathbb{F}_2^n$). As usual, the automorphism group of $C$ is the subgroup of ...
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2answers
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1answer
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### Length of the transversal for surfaces with cusps

In Peter Buser's Geometry and Spectra of Compact Riemann Surfaces he shows that the length of the transverse curve to a geodesic in a pants decomposition on a compact hyperbolic surface has length a ...

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