# Questions tagged [reference-request]

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

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### Does this category has a computable algebraic K-theory

This question is inspired by this post. I decided to make some order in my very limited knowledge in algebraic K-theory. Let me start with the commutative case: $R$ is a commutative ring. $Perf(R)$ ...
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### Character degrees in induced blocks

Let $G$ be a finite group and $U\leq H\leq G$ a chain of subgroups. Presume that $p$ is a prime dividing the order of $U$. Suppose that $b_1$ is a $p$-block of $U$ and $b_2$ a $p$-block which is ...
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### Infinite composition of continuous functions

Let $f_n:\mathbb{R}\rightarrow \mathbb{R}$ be a sequence of functions and define $F_n:= f_n\circ \dots\circ f_1$. Then $F_n$ is continuous. However, the pointwise limit need not be (consider Mateusz'...
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### Arthur's Simple Trace Formula

In Deligne–Kazhdan–Vigneras's "Représentations des groupes réductifs sur un corps local," they use the Simple Trace Formula to prove cases of the local Jacquet–Langlands correspondence ...
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### Counting unions of unlabelled connected graphs

My question can be stated as follows: let $X$ be a hereditary family of unlabelled graphs closed under disjoint unions. Suppose we know, for each $n$, the number $c_n$ of connected graphs in X on $n$ ...
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### Checking existence of proofs of fixed length

This question is a continuation of a related previous question (check here). Let $\mathcal{L}$ be a recursive first-order theory with the Hilbert-Ackerman's proof calculus, and such that the ...
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### Are orbit polytopes of rotation subgroup of Coxeter group combinatorially equivalent?

Suppose that $G\subset O(d)$ is a finite reflection (finite Coxeter) group. For any $v\in \mathbb{R}^d$ which is not fixed by any non-trivial $g\in G$, one can consider the orbit polytope (Coxeter) ...
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### Reference on Fourier analysis on compact groups

I am looking for a reference for Fourier analysis on compact (Lie) groups. The kind of theorems I would like the book to cover/do are the Peter-Weyl theorem, define Fourier transforms and use the ...
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### bijection mapping a transversal to a transversal

The following must certainly be a standard result, so what I'm looking for is a reference, or the name of this theorem. I don't have any combinatorics books at my fingertips, but I could see this ...
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### regularity of the solutions of Prandtl equation on the segment

Let $p(x)$ be a positive measurable function on $(-1,1)$. Consider the Prandtl equation $$u(x)-\frac{p(x)}\pi \int_{-1}^1 \frac{u'(t)}{t-x}dt=p(x)h_0(x),\quad u(1)=u(-1)=0.\quad\quad(\star)$$ What ...
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### On $(2,3)$-generation of finite simple classical groups

A group $G$ is called $(a,b)$-generated if $G=\langle x,y\rangle$ for some $x,y\in G$ with $|x|=a$ and $|y|=b$. I know some of the histories on this problem. For example, in this early paper in 1996 ...
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### A royal road to Coulomb branches of 3D $\mathcal{N}=4$ gauge theories

So, I've been very interested recently with the developements of the (now mathematically precise) theory of Coulomb branches - in particular because of its recent applications on representation theory ...
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### Trees of prescribed ordinal

My question is very imprecise, as I know very little about descriptive set theory. In a problem I am thinking about I have a family of well-founded trees (finite sequences on $\cup_n X^n$ closed under ...
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### Searching for theorems characterizing when $O_p(G)$ is trivial / non-trivial

Let $G$ be a finite group. Let $p$ be a prime. Let $O_p(G)$ be the $p$-core of $G$. Are there any theorems known saying something like $O_p(G)$ is trivial, if and only if ... and $O_p(G)$ is non-...
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### Bounding Greens function matrix elements in terms of the diagonal elements

Consider the Hilbert space $l^2( \mathbb{Z}^2)$ and suppose that I have a unitary band matrix. I.e. $\langle e_j , U {e_k} \rangle = 0$ for say $\vert \vert j-k \vert \vert > 2$ (in say taxi-cap ...
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### How are these “Voronoi-dual” configurations called?

If $\mathscr P\subset \mathbb R^d$ is a discrete point configuration, take the Voronoi diagram of $\mathscr P$ and call $\mathscr P'$ the vertices of that diagram. I would like to know if ...
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### Bijective proof of a combinatorial identity: $\sum\limits_{k=0}^n\binom nk^2 \binom k{n-m}=\binom nm \binom{n+m}m$

Identity \begin{equation} \sum_{k=0}^n\binom nk^2 \binom k{n-m}=\binom nm \binom{n+m}m \tag{1} \end{equation} was used in an answer here. As shown in that answer, (1) easily reduces to \begin{...
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### Is there any good reference on the Bayesian view that can be helpful for reading papers on the number theory using heuristic arguments?

Nowadays there are many papers on the number theory using heuristics. I have read some of them. But I have no clear understanding of the Bayesian Probability(subjective probability). The concept of ...
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### Homotopy group action and equivariant cohomology theories

Many of the introductory notes on generalized equivariant cohomology theories assume that one is working over the category of $G$-spaces or $G$-spectra. However, one thing that concerns me is that the ...
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### Permanent of a Kronecker product of matrices

It is well known that $\det(A \otimes B) = \det(A)^m \det(B)^n$ when $A$ and $B$ are square matrices of size $n$ and $m$ where $\otimes$ denotes the Kronecker product. Question: Is there a similar ...
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Consider the ODE $$\begin{cases} x''(t) + \sin (x(t)) = u(t) \\ x(0)=x_0\\ x'(0)= x_1 \end{cases}$$ and the problem of minimizing $$J(u) = \int_0^T |x(t) - \bar x|^2 dt + \int_0^T u^2(t) dt$$ for $... 2answers 562 views ### Élie Cartan's paper “Les groupes réels simples, finis et continus” of 1914 Question 1. Does Élie Cartan's paper Les groupes réels simples, finis et continus, Ann. Sci. École Norm. Sup. (3) 31 (1914), 263–355 contain a classification of$\Bbb C$-linear involutions of simple ... 0answers 122 views ### On classifying groups of order$p^5$Can someone suggest me some source where the author has classified all non-isomorphic groups of order$p^5$? I need complete classification (not upto isoclinism), and also in finitely presented form .... 2answers 144 views ### Convergence of conditional measures for a convergent sequence of probabilities whose projection is constant Setting Suppose$\mu_n$is a sequence of probability measures on$[0,1]\times [0,1]$converging to a limit probability$\mu$meaning that $$\lim_{n\to+\infty}\int f(x,y)d\mu_n(x,y) = \int f(x,y)d\mu(... 0answers 136 views ### Pseudoreflection groups in affine varieties Suppose \mathsf{k} is an algebraically closed field of zero characteristic. Chevalley-Shephard-Todd (C-S-T) Theorem in one of its equivalent versions is the following result: (C-S-T): Let G be a ... 0answers 163 views ### When did the main conjecture in Vinogradov's mean value theorem first appear in literature? Recently I was asked about the history of Vinogradov's mean value theorem that I was hoping someone here could clarify. Let me first start with some terminology. Let J_{s, k}(X) be the number of 2s... 1answer 245 views ### Good overviews on \phi^{4}-field theory? I'm looking for nice overviews on \phi^{4}-field theory from the mathematical-physics point of view. To be a little more specific, here are some topics I'd like to read about: (1) What are the ... 1answer 265 views ### Minimum cardinality of a cofinal collection of countable subsets of a set Setup Let X be a set of cardinality \kappa\geq \aleph_0. Edit: Based on Todd Eisworth's suggestion: What is the minimum cardinality of a collection \hat{X} of countable subsets of X such that ... 1answer 71 views ### Directed graph minor theorems In proving the graph minor theorem, Robertson and Seymour proved a stronger statement, namely that the directed graph minor theorem is true, using the definition A directed graph is a minor of ... 1answer 237 views ### Rational homotopy invariance of algebraic K-theory Suppose that R\to S is a 1-connected morphism of connective structured ring spectra that induces an isomorphism on rational homotopy groups. Is the induced map of (Waldhausen) K-theory spectra$$ K(... 1answer 100 views ### Faithful representation of group of order$p^4$In the (xi) group of the classification of groups of order$p^4$given by W.Burnside in his book, "Theory of groups of finite order". The group ($\mathbb{Z}_{p^{2}}\rtimes \mathbb{Z}_{p^{}}) ...
Let $(X,d)$ be a metric space, $\mathcal{B}$ the Borel $\sigma$-algebra on $X$, and $\mathcal{M}(X)$ the space of totally finite measures on $\mathcal{B}$. Let $\|\mu\|_{TV}$ be the total variation ...