All Questions

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Mathematic Theory of Computation [on hold]

Let Sigma be an alphabet. Use the principle of induction on Sigma^*, to prove that |w v| = |w| + |v| for all w, v in Sigma^.
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Asymptotics of the multipartition function

Recall that the multipartition function $p_k(n)$ counts the number of $k$-tuples of partitions $\lambda^1,\ldots,\lambda^k$ of numbers $a_1,\ldots,a_k$ with $a_1+\cdots+a_k=n$. It has a generating ...
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Is there a Ladner's Theorem" for the PH-vs-PSPACE scenario?

Like a statement of the kind, If the Polynomial Hierarchy (PH) $\neq$ PSPACE then there exists $L \in PSPACE \backslash PH$ which is not PSPACE-complete"? Or is there something else that states ...
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A 2D random walk on a lattice of equilateral triangles [on hold]

Calculate the characteristic ratio C∞ for a random chain on a two-dimensional lattice made of equilateral triangles with side a. At each step, a walk has five choices (it cannot double back).
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How to fit a stochastic matrix to given data.?

Given a data sequence of noisy observations of a 3-state Markov chain $X$ -- $y_1$,$y_2$,...$y_n$, with two transition matrices $A_1$ and $A_2$ corresponding to different regions (**) in the (unit) ...
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Lawvere algebraic theory as presentation-invariant [on hold]

We can read in a lot of papers, included Lawvere's PhD thesis, that algebraic theories are "an invariant notion of which the usual formalism with operations and equations may be regarded as a ...
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In search of a preprint by Litherland

I've seen the following citation a lot: "R. LITHERLAND: A formula for the Casson-Gordon invariants of a knot, preprint." I can't seem to find a corresponding publication. [Added in edit: apparently ...
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double Sum with a function of 3 variables inside. How to solve it? [on hold]

I am studying time scheduling problem solving with linear programming. I am reading paragraph 2.5 from this book (pages 32-35) and I am trying to solve it with Java. I have some questions about ...
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Establishing Duality in Tannakian Categories

I sometimes need to prove a category is Tannakian. Part of the definition of a Tannakian category is that it is rigid. However, I find the definition of rigid categories somewhat difficult. I don't ...
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Replacing functors by topologically or simplicially enriched functors

I believe it is true that if a functor $F:Top\to Top$ preserves weak homotopy equivalences then it is related by a natural weak equivalence to some other such functor that is in some sense continuous, ...
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C^*-algebras and bidual [on hold]

Let $A$ be a C$^*$-algebra, $x \in A$ a non-zero positive element of $A$, $r(x)$ the range projection of $x$ in $A^{**}$ and $e = 1 - r(x)$. How do I show that exist a projection $f$ in $A^{**}$ such ...
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Motivation of $a_p$ for non-CM elliptic curves [on hold]

For an elliptic curve $E$ without CM let $\overline{E}$ be the good reduction of $E$ modulo $p$ prime. The value $a_p = p+ 1 - \mathbb{F}_p$ is referenced by DDT on p.19 and Ribet on p.5 . However ...
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Simple example game with 3 players [on hold]

I am currently writing an algorithm to compute different things as nash equilibria, dominated strategies etc for normal-form games. Since I am now trying to extend it to an infinite amount of players, ...
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Limits at infinity of fellow-travelling sequences in Teichmuller space,

I have a question concerning limits of sequences of points in Teichmuller space, and how this notion is preserved under fellow-travelling. Suppose that we have closed surface of genus $g\geq 2$, and ...
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local rings with finite type maximal ideal

Let $A$ be a local ring with a maximal ideal $\mathfrak{m}$ finitely generated (not principal). Is there a sufficient condition for $A$ to be noetherian? For example, we know that the completion ...
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A reference for $\mathbb{A}^1_R$ being a coarse moduli space of the stack of elliptic curves

Let $R$ be a ring and let $\mathcal{M}_{1, R}$ be the algebraic $R$-stack of elliptic curves (over $R$-schemes as bases). One knows that the coarse moduli space of $\mathcal{M}_{1, R}$ is supposed to ...
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Fixed area, largest mass — is there a name?

Let $x\in \mathbb{R}^n$ and let $s_k(x)$ denote the sum of the $k$ largest entries of $x$. The function $s_k(x)$ is well-known to be convex and is often used in optimization, such as ...
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What other books are like these?

A certain class of books is defined as follows: (1) the book was kept for years in a cafe or mathematics library; (2) the primary contents are research problems and comments, handwritten by resident ...
Is there a function $g(s)$ such that if there is a set of numbers $\{r_i\}_{i=1}^m$ such that $r_i\bmod p_j\in\{0,1\}$ at every prime in $\{p_j\}_{j=1}^n$ such that $2^t\bmod p_j\neq1$ at every ...