# All Questions

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### generic divisibility equation for two natural numbers [on hold]

Given two natural numbers N and B, so that N > B, is there a generic equation that contains only multiplications of N and B which can tell whether N is divisible by B? Basically, something like a ...
43 views

### Combinatorial interpretation for coefficients of reciprocal of power series

I've seen a number of combinatorial interpretations for the coefficients of the compositional inverse (aka reversion) of a power series. Is there a known combinatorial interpretation for the ...
21 views

### Simplify a Trigonometric equation [on hold]

Should end in Sin(a)+Cos(a) I'm unable to decrpyt it.
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### Confusion regarding statement of mirror symmetry for elliptic curves

I am a little bit unsure about the mirror symmetry statement for elliptic curves; specifically, how the flipping of the Kähler and complex moduli works. Perhaps I should say at the outset, the reason ...
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### Integral of Daubechies wavelets

For Daubechies wavelets according to this paper (above eq 19) this relation holds $$\int_{-\infty}^{-\infty} \phi(2x-i)\phi(2x-j)dx = \frac{1}{2} \int_{-\infty}^{-\infty} \phi(x-i)\phi(x-j)dx$$ ...
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### Number Theory Characterization Problem

Given any natural number $N = a_{n}a_{n-1}\ldots a_{1}$, let us associate to it the set $S_{N} = \bigcup_{j=1}^{n}\{(a_{j},j)\}$. We're going to define a d-self-contained number as any natural number ...
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### Homology of inverse limits over inverse systems more complicated than towers

Most textbooks discussions of homology of inverse limits of chain complexes consider only “towers,” i.e. inverse systems indexed by the natural numbers. I’d like to find a reference that explains what ...
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### Questions related to a summation of fraction equation

I am struggling the following problems. It is not ensured to solve completely because these problems are generated by myself. Particularly, I guess the second problem is very hard if we try to solve ...
42 views

### Is there a name for groups of the form $Sp(1)^n$?

A (compact) torus is a Lie group isomorphic to the product of finitely many circles: $T^n = S^1 \times \cdots \times S^1$. Such groups are extremely important in Lie theory, Differential Geometry, ...
69 views

### estimating binomial coefficients

There is a beautiful paper on the arXiv by Andrew Suk containing an asymptotic result about the Erdös-Szekeres convex polygon problem. I am struggling with one of the estimates he makes on page 4. He ...
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### How many vertical or horizontal asymptotes does this equation (x^2 - 1)y = x^2 - 4 have? [on hold]

How many vertical or horizontal asymptotes does this equation (x^2 - 1)y = x^2 - 4 have? Actual question is this(Qs11) Answer is given as C but I think there are two horizontal asymptotes
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### Constructively, are all fibrations cloven?

A "cloven fibration" is a fibration for which we have an explicit choice of cartesian liftings; this is often phrased as, "We can pick a lifting without using the axiom of choice". Firstly, I'm a bit ...
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### Permutation Invariant Color Class

$G$ is a $d$ regular graph, it has $n$ vertices. $S_n$ acts on $n$ vertices of graph $G$. Question: Does there exist a coloring algorithm for which color classes is invariant under all ...
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### Symmetries of modular categories coming from quantum groups

This is a request for references about the computation of the braided autoequivalences of fusion categories coming from a quantum group. I could not find even the description of braided ...