# All Questions

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### Matching in the Boolean Algebra

We consider the Boolean Algebra of the set $[n]=\{1,\dots,n\}$ and the matching $\psi$ from the $m+1$ subsets of $[n]$ into the $m$ subsets of $[n]$ for $(n+1)/2\leq m+1\leq n$, which is used to show ...
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### Where are there defined objects between gerbes and bundle gerbes?

Consider a special kind of/something like a gerbe where there is first given local trivialization data with equivalence over 2-fold overlaps but not isomorpphism. Does this exist in the literature?
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### Characterization(?) of coersive(?) elements in the special linear group

Take your favorite matrix norm $\|\bullet\|$ (my favorite is the Frobenius norm $\|A\| = \sqrt{\operatorname{tr} A A^t}$). Now consider the set $S_x$ of matrices $A,$ such that $\|A\| < x$ and ...
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### Unexpected $\sqrt{3}$

A somewhat lengthy calculation, involving integrals, reveals that the probability an $n\times n$ Hermitian matrix, drawn from the Gaussian unitary ensemble, is positive definite, decays as ...
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### Euler number of the complex of basic forms

Let $G$ be a compact Lie group and $\pi:P \to M$ a principal $G$-bundle. I would like to understand the geometry of $M$ through $P$ with the $G$-action. I am trying to understand the Hopf bundle ...
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### Links between Geometric Group Theory and Number Theory

Do You know any successful applications of the geometric group theory in the number theory? GTG is my main field of interest and I would love to use it to prove new facts in the number theory.
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### bound for $|E[\frac{X}{Y}]−\frac{E[X]}{E[Y]}|$

Is there some bound for $|E[X/Y]−E[X]/E[Y]|$ ? Here $X$ and $Y$ are both summation of a fixed number of Bernoulli random variables and a constant that is >0, which is to guarantee that the denominator ...
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### Homology of infinite intersection

If $X_1\supseteq X_2\supseteq \ldots$ is a sequence of "nice" compact spaces, I would like to know whether the natural map from $H_*(\cap X_i)$ to the inverse limit $\lim \, H_*(X_i)$ is surjective. ...
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### Variations to Cayley's Embedding Theorem for Groups

Early in a course in Algebra the result that every group can be embedded as a subgroup of a symmetric group is introduced. One can further work on it to embed it as a subgroup of a suitable (higher ...
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### Abstract Algebra [migrated]

Show that a group that has only a finite number of subgroups must be a finite group.(Fraleigh, A First Course in abstract Algebra-7th Edition,pg.67) I could not show properly so I need help. Thank ...
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Are there necessary/sufficient conditions for a functor $f\colon \mathcal C\to \widehat{\mathcal A}$ to induce an equivalence $\text{Lan}_yf=F\colon \widehat{\mathcal C}\leftrightarrows ... 3answers 144 views ### Existence of nonergodic polygonal billiard Let$P$be a polygon in the plane. One can define the billiard flow on the unit tangent bundle of$P$, just following the trajectories of the billiard at speed one. A standard conjecture is that a ... 0answers 30 views ### Maximum chi-square distance between norm vectors [on hold] What is the maximum possible chi-square distance between two normalized vectors? The representation of chi-square distance is below.$d(x,y) = \sum_i \frac{(x_i-y_i)^2}{x_i+y_i}$1answer 92 views ### Kaehler form on weighted projective space The Kaehler potential for the standard Fubini-Study Kaehler form in projective space$\mathbb{C} P^n\$ is given by: $$\log(\sum_{i=0}^n |z_i|^2)).$$ What is the analogous formula for a Kaehler ...

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