# Questions tagged [reference-request]

This tag is used if a reference is needed in a paper or textbook on a specific result.

9,738
questions

**2**

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39 views

### Provenance of a result on regular simplices with integer vertices

There are several MO questions related to the question of characterizing those integers $n$ for which there exists a regular $n$-simplex in $\mathbb{R}^n$ with integer vertices, e.g., coordinates of ...

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16 views

### Feasibility criteria in Integer Linear Programming

Consider an integer linear programming problem:
For $A\in M(m, n, \mathbb{Z})$ and $b\in \mathbb{Z}^m$
find $x=(x_1,\ldots,x_n)^T\in \mathbb{Z}^n_{\geqslant0}$ such that $Ax=b$.
Sometimes one ...

**1**

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**1**answer

32 views

### Reference request for (weak*) metrizability of a bounded space of signed Radon measures on a compact set

I know the following is true and I know how to prove it (cf. exercise 50 on page 171 in Folland, Theorem 7.18 in Folland), but per my adviser's instructions, it would be better to find a source to ...

**4**

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30 views

### Quantitive and computational improvement of the Oseledets multiplicative ergodic theorem for irrational rotation

Consider irrational rotation $T:S^1\to S^1, T(x) = x + \alpha$ where $\alpha\notin \mathbb{Q}$ (you may assume additional number theoretic properties of $\alpha$, say $\alpha = \sqrt{2}$ is already ...

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225 views

### A (surprising?) expression for $e$

I apologise if this is off topic.
Consider the quantity
$$
F(m,n,k)=\frac{(m)_k}{k!n^{k-1} }
$$
where $m,n \in \mathbb{N}.$ For moderately large $n$, it seems that the approximation
$$
\sum_{k=1}^{K} ...

**2**

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**1**answer

74 views

### Uniqueness of presentation for semi-abelian varieties

Let $k$ be any field and $G$ a semi-abelian variety over $k$, i.e., an algebraic group that fits into an exact sequence
$$ 1 \to T \to G \to A \to 1$$
of algebraic groups, where $T$ is an algebraic ...

**4**

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69 views

### Is a presentation of the hyperbolic orthogonal group of rank 2 over the integers known?

The hyperbolic orthogonal group $O_{g,g}(\mathbb{Z})$ often appears in the study of high-dimensional manifolds, see e.g. work of Kreck or Galatius and Randal-Williams. Let $H$ denote the lattice $\...

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31 views

### Reference request for solving pde numerically

What is the reference should i read to solve this pde numerical ?
$$\frac{\partial u}{\partial t} - r (\frac{\partial^2 u}{\partial x^2}+\frac{\partial^2 u}{\partial y^2})+\sin(y)\frac{\partial u}{\...

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23 views

### Beck-Fiala Discrepency Type Results for Arbitrary Graph Labelings

Suppose we have a graph $G$ on $n$ vertices $x_1 , \dots, x_n$ attached with weights of values from $1$ to $n$. We will write $\text{weight}(x_i)$ as simply $x_i$ and let $\text{diff}(G) = \min _{(x_i,...

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75 views

### Independent conditions imposed by a collection of double points

Let's consider the following statement : There exist a collection of $d$ points $\gamma \subset \mathbb{P}^{n}$, so that $h_{\Bbb P^n}(\gamma^{2} ,m) = \min\{(n+1)d, \binom {n+m}{n}\}$ implies for any ...

**0**

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26 views

### Neumann equation on manifold with edge or corner

Let $(M,g)$ be a compact Riemannian manifold with boudnary and corner, i.e. locally mdoelled in $[0,\infty)^1\times \mathbb R^{n-1}$ or $[0,\infty)^k\times \mathbb R^{n-k}$, where $n=\dim(M)$.
...

**1**

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57 views

### Defining pull-back of Chow groups under a morphism of special type

Let $X$ be a normal complex projective variety (not necessarily smooth), and let $Y$ be a smooth complex projective variety. Let $Z\subset X$ be a smooth closed subvariety.
Let $\pi : Y\rightarrow X$...

**3**

votes

**1**answer

128 views

### Mapping Problems to Boolean Formulas for SAT Solvers

I came across Marijn Heule and Oliver Kullmann's paper on recent techniques in highly efficient SAT solvers. In particular they describe the Pythagorian Triple Problem, which they solved using that ...

**0**

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56 views

### Spectra of one dimensional Schrodinger operators [on hold]

I am trying to understand how to compute the spectra of one-dimensional Schr?dinger operators $$
\mathcal{L}:=-\partial_x^2+V,
$$
where $V$ is a bounded function in the whole line. I am particularly ...

**7**

votes

**1**answer

381 views

### Reference request: The unit of an adjunction of $\infty$-categories in the sense of Riehl-Verity is a unit in the sense of Lurie

I'm looking for a reference (or proof) for the statement given in the title: that when we have an adjunction between quasicategories in the sense of Riehl and Verity (defined e.g. in Section 4 of ...