# All Questions

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### In how many ways (up to isomorphism) can we merge two graphs?

Let $(V_1,E_1)$ and $(V_2,E_2)$ be two graphs with $|V_1|=n_1$, $|V_2|=n_2$, $|E_1|=m_1$ and $|E_2|=m_2$. The question is how to count the number of distinct (i.e. up to isomorphism) mergers of the ...
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### When do powers and ends in functor categories act pointwise?

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### Trouble with an assignment [on hold]

Can anyone please be kind enough to help me with this. On one shelf there are 5 hardcover books and 6 paperbacks and on the other shelf there are 7 hardcover and 4 paperback. From the first shelf ...
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### Markov Modulated Markov Chain

Consider a discrete time Markov chain $X_t$ on some finite state space $\mathcal{S}$ with transition matrix $P$. Now consider a process $Y_t$ also on $\mathcal{S}$, which conditioned on $X_{t}=s$ ...
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### Moduli space of complex Tori

Is there any explicit computation for the Weil-Petersson metric on moduli space of Tori of complex dimension n?
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### How big are the prime factors of $2^kp - 1$?

I have already asked this question here. No answers despite the bounty (which has now ended) Let $p$ be a prime number, $p > 3$. Does there always exist $k \in \mathbb N_{\ge 1}$ such that the ...
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### The derivatives of Riemann xi function [migrated]

What are the first few values of derivatives of Riemann xi function at zero? Is there any general formula for calculating the nth derivative of the riemann zeta function at zero? What happens to the ...
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### clustering permutations by shared subsequences [on hold]

I have a question, stimulated by some biology, about comparing sets of permutations. The problem Let's think of genes on a bacterial chromosome as beads on a string - atomic, unique objects, with ...
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### How many times does a simple symmetric random walk of length n return to the origin?

Consider the simple symmetric random walk on the integers starting from the origin of length $n$. More precisely, I will denote an $n$ step random walk $w$ as  w:= \omega_0 \omega_1 \ldots ...
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### Context Free Languages closed under Kleene Star? [on hold]

I'm looking at the proof for the closure property of CFL under kleene star and I'm having a little trouble understand what it means. From what I saw this is the proof: ...
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### Inverses of probability generating functions: positivity of derivatives

Let $\mathcal{G}$ be the set of probability generating functions of random variables taking positive integer values, considered as functions on $[0,1]$. So $G\in\mathcal{G}$ can be written ...
I am currently reading a proof where the $\pi-\lambda$ Lemma and the monotone class theorem are applied to show a certain property for bounded random variables. The author of the book always shows the ...
Let $Y$ an affine finite type scheme over an algebraically closed field $k$. Let $S$ be a closed subscheme of $Y$ and $Y'$ the henselization of $Y$ along $S$. If we have a $\mathbb{Z}_{\ell}$ local ...