# 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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### Alternative Mersenne numbers

Let $\ b\in\mathbb Z,\$ and $\ |b|>1.\$ Call $$M_b(n)\ :=\ \frac{b^n-1}{b-1}$$ to be $n$-th Mersenne number mod $b$. The necessary condition for $\ M_b(n)\$ to be a prime is that $\ n\$ is a ...
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### Does Borel fixed-point theorem hold for Deligne-Mumford stacks?

Let $X$ be a proper Deligne-Mumford stack over $\mathbb{C}$ with an action by a complex torus $T$. Let $X^T$ denote the fixed locus. Question: Is the following statement true? ...
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### What to do with antique/older mathematics books? Throw away or something else? [duplicate]

My father, who held 4 post graduate degrees and was a lifetime student, passed away recently. He has an entire bookcase full of older mathematics books, including some on related topics such as ...
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### Two types of the Germain prime siblings

Let $\ p\$ and $\ q:=2\cdot p+1\$ be primes — they are called Germain prime siblings. Such a pair belongs to the first type $\ \Leftarrow:\Rightarrow\ \frac{q^2-1}8\equiv\pm1\mod8,\$ and to the ...
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### Product and coproduct in derived category

I'm sure this is either a standard result or false, but I don't have enough experience with the derived category to decide either way. I have tried looking in Kashiwara-Schapira's Sheaves on Manifolds ...
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### Relations between LR coefficients and cores and quotients of partitions

I have a formula for certain coefficients in terms of Littlewood-Richardson coefficients and $p$-cores and $p$-quotients of partitions ($p$ is a prime). I would like to obtain some positivity ...
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### Expected diameter of a random point set

General problem: For a point set $S\subset X$ in a metric space $(X,d)$, let $\text{diam}(S)=\max_{x,y\in S}d(x,y)$. Given a distribution $P$ on $X$ and $m$ i.i.d. points $x_1,\ldots,x_m\sim P$, what ...
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### On convergence of entire functions

Suppose we have a sequence of entire functions $f_n$ such that $$\text{f_n(z)\to0 for each natural z}\tag{1}$$ (as $n\to\infty$). Is it possible to give general additional conditions on the ...
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### Total sum of squares of characters of the symmetric group $\mathfrak{S}_n$

In my earlier MO post, I proposed the double sum $\sum_{\mu\vdash n}\sum_{\lambda\vdash n}\chi_{\mu}^{\lambda}$ regarding characters of the symmetric group $\mathfrak{S}_n$. Soon after, I started ...
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### Name of an inductively defined sequence of graphs

Let $G_k$ be the graph obtained by applying the following procedure k-times: Start with a graph with single vertex $v$ (Call this graph $H$) Add a vertex $u$ such that $u$ is not adjacent to any ...
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### Does the following corollary of Mackey's tensor product theorem hold for smooth representations?

Let $G$ be a locally profinite group, and let $H$ be a closed subgroup of $G$. Let $\sigma$ be a smooth representation of $G$, and let $\tau$ be a smooth representation of $H$ (henceforth, every ...
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### Reference request: Pascal type octagon theorem

I am looking for a reference to a generalisation of the celebrated hexagon theorem of Pascal which states that if $A$, $B$, $C$, $A_1$, $B_1$ and $C_1$ are the (distinct) vertices of a hexagon in ...
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### Reference request: Moore graphs

It is clear that the term Moore graph was coined by Hoffman and Singleton in their paper On Moore graphs with diameters $2$ and $3$, where they write E. F. Moore has posed the problem of describing ...
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### A random process with conserved momentum: 'particle decay'?

Consider a particle $p_1$ moving at unit speed along a straight line in $\mathbf{R}^2$, directed by some vector $v_1 \in \mathbf{S}^1$. Equid this particle with a Poisson clock $\tau_1$, with ...
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### Should every modern day mathematician care about category theory? [closed]

As far as I know, category theory is used mainly in topology. I have a dislike towards category theory, similar to my dislike of Bourbakism, and want to avoid it as much as I can. However, the head of ...
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### A strong Borel selection theorem for equivalence relations

In Kechris' book "Classical Descriptive Set Theory" there is the following theorem (12.16): Let $X$ be a Polish space and $E$ an equivalence relation such that every equivalence class is ...
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### Explicit homotopy for Hochschild chains from natural isomorphism

Let $A,B$ be $k$-linear (possibly, dg-)categories, let $f,g:A\to B$ be two linear functors, and let $T:f\Rightarrow g$ be a natural isomorphism. If one denotes by $C_\bullet(A,A)$ the standard ...
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### Central limit theorem for weak correlated random variables

I have a sequence of weak correlated continuous random variables $\{X_i\}$ with bounded variance and $\operatorname{Cov}(X_i,X_j)\rightarrow0$ for $|i-j|\rightarrow\infty$. I was able to find a ...
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### Has the von Neumann entropy ever been used in classical mechanics?

After going through an application of the von Neumann entropy(from quantum information theory) to certain problems in computational neuroscience , it occurred to me that this entropy might have ...
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### Stallings' binding tie

I came to know that the statement below could be proved using Stallings' binding tie argument, though I have no reference article proving the statement by the binding tie argument. Can anyone help me ...
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### A diophantine equation involving partial sums of exponentials similar than the equation in Fermat's Last Theorem

I'm curious about the following diophantine equation from my invention: I don't know if this is in the literature, I wrote it using creativity in an attempt to write a variant of the equation in ...
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### Leray-Schauder degree in Banach manifolds

The so called Leray-Schauder degree is usually defined for maps of the form $I - f$, where $f: X \to X$ is a compact map defined on a Banach space. Is there an extended definition for the setting of ...
Let $\overline{\widehat{Z}_i} = \frac{E_i\left[ \int_{t_i}^{t_{i+1}}\widehat{Z}_sds\right] }{\Delta t_i}$ with $\widehat{Z}$ a square integrable process, $\Delta t_i := t_{i+1} - t_i$, and $E_i$ ...
In Theorem 1 of  we have the following result: Let $D$ be a real $n \times n$ diagonal matrix and consider the rank-one modification $C = D + \rho z z^T$, where $\rho > 0$ is a real scalar and \$...