# All Questions

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### Genus of Tutte-Coxeter Graph

What is the genus of the Tutte-Coxeter graph -- the incidence graph of the GQ of order 2? Seems like it should be well known, since nearly every other parameter for that graph is known, but I can ...
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### Showing coercivity condition for an enery functional

Consider the energy functional $e(\cdot)$ \begin{align*} e(f,Q)&=\int_a^b \bigg\{f^4\bigg[1+\|\frac{d}{dr}Q\|^2+f^2\dot f^2\bigg]\bigg\} \,dr, \end{align*} over the space of \begin{equation*} ...
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### Sequence of n numbers and arithmetic means [on hold]

I'm struggling with this exercise: Prove that sequence of n numbers 1,2, ..., n can be arranged to sequence where arithmetic mean of any two numbers is not between those two numbers. For example: ...
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### Is there a holomorphic Morse-Bott lemma?

It asks for a generalization of the question in the post Normal form for a holomorphic Morse function Suppose $f$ is a holomorphic function on a complex manifold $M$ which has Bott type critical ...
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### Can the same number be generated by multiplying two different pair of primes? [on hold]

Let's say I have four different prime numbers: A B C D. Is there any combination of primes that makes the following equation true: A * B = C * D
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### Phillips-Sarnak conjecture in higher dimension

The Phillips-Sarnak conjecture states that for a generic Fuchsian lattice the space of Maass cusp forms is finite-dimensional. Generic here means in particular non-uniform, non-arithmetic, no special ...
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### Counting categories with at most $n$ morphisms

There are a number of results which count the number of possible algebraic structures on a set of $n$ elements. Notable previous MO questions are for example here and here. The analogous question for ...
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### Are n-truncated quasicategories a model for n-categories?

In Higher Topos Theory, Lurie gives a description of $n$-categories (section 2.3.4) in terms of quasicategories. In other words, he gives a definition (2.3.4.1) of an $\infty$-categorical notion of ...
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### Rational points in the Alexandroff line

Let $X$ be the subset of the long line consist of rational points with the topology inherits from the long line. Is $X$ a metrizable space?
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### Positive Fourier coefficients for a function $f:\{+1,-1\}^n \to \mathbb R$

This is from my research in computer science where the Fourier transform over $GF(2)^n$ is a tool to study functions on the Boolean hypercube. For example, the majority function on 3 variables is ...
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### Does the following first order approximation of the Kapranov-Vasserot infinitesimal loops still do any job?

Let $X$ be a scheme over, say, a field $k$. Let us denote $\mathrm{Spec}(k[\varepsilon])$ by $T$ and its (unique) $k$-point by $0\in T$. Call the first order infinitesimal cone $C_{T,0}(X)$ over $X$ ...
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### n-body systems and bifurcations

From what I understand, in bifurcation theory, one definition of the equivalence of two dynamical systems is that they are topologically equivalent. However if say proteins A, B start out as straight ...
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### Invertibility of NxN nonnegative matrix with diagonally dominant elements [migrated]

I have a NxN nonnegative matrix where the diagonal element of any row i is greater than the off diagonal elements, 1 > aii > aij ≥ 0 for j not equal to i . This not a diagonally dominant matrix as it ...
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### Do these systems of Diophantine equations have solutions? [on hold]

Me what's interesting. These formulas describe any decision or not? If not, what ideas have towards a rest? The system of equations: ...
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### How to rank a separate population using elo points/system [on hold]

Background: I have a website where students vote on the attractiveness of their peers: they are presented with two images, and they must pick one (the "winner")- then the elo score for each is ...

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