# All Questions

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### When is the kernel of a semi-module homomorphism a partitioning sub-semi-module?

I would like to identify a representation of the subcategory of a comma category of semi-rings, whose objects are abelian group objects. When attempting to identify the representation, the following ...
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### Looking for a handy inequality, Cauchy-Schwarz-style

I am interested in upper bounds for the following ratio: $$\frac{n\sum_{i=1}^{n}{x_{i}}}{\sum_{i=1}^{n}{x_{i}^{2}}}.$$ In terms of Reznick's paper Some inequalities for products of power sums that ...
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### Irreducible polynomials in $\mathbb{Q}_p((X))[Y]$

I'm looking for some criteria for the irreducibility of polynomials with coefficients in $\mathbb{Q}_p((X))$. In particular, is the polynomial $Y^2+1$ irreducible over $\mathbb{Q}_3((X))$? And how ...
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### Planar algebraic translation of a subfactor property

Let $N \subset M$ be an irreducible finite depth and finite index subfactor. $M$ is a completely reducible (algebraic) $N$-$N$ bimodule, it decomposes into irreducibles as follows : ...
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### How do most people write permutations?

I'd like to know how people prefer to write permutations, or elements of the symmetric group $S_n$ for $n\ge0$. The most natural way to define a permutation in $S_n$ is as a bijection on the set ...
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### Is set packing easier when the sets are squares?

I am interested in the following problem: ...
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### Analytic continuation of Arithmetic function

Given an Arithmetic function, (or even better who's values are integers), how can I tell if it has an Analytic continuation to the whole plane, or maybe half plane? I guess it might be too general a ...
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### Is mod p Hecke algebra gorenstein? [on hold]

Barry Mazur proved a certain Hecke algebra T is gorenstein in his famous paper Eisenstein Ideal. Now Wiles proved that T is a complete intersection, too, so T/pT is also complete intersection by ...
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### Representation-theoretic operations on modular forms

Let $A$ and $B$ be Hecke eigenforms of some weight $k$ and level $N$. We know that there are irreducible representations $\rho_a$, $\rho_b$ of the absolute Galois group of $\mathbb{Q}$ whose trace of ...
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### Intermediate submodels and the continuum hypothesis

Let $V$ be a model of $ZFC+GCH$ and let $V[G]$ be a generic extension of $V$ in which $CH$ fails. Question 1. Is there a model $W$ such that: 1) $V \subseteq W \subseteq V[G],$ 2) $W\models CH,$ ...
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### A probability/counting question

Suppose you have $(\Omega,\mathcal{B},\mu)$ a finitely additive atomless probability algebra. Then say you have an infinite collection of sets $(B_i:i\in\mathbb{N})$ in $\mathcal{B}$ such that for ...
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### Why is there no product type in simply typed lambda-calculus?

Consider simply typed $\lambda$-calculus that has only the unit type as primitive. We would like to encode the product and the sum types. An encoding of the product type in the untyped ...
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### $\text{mod} \, p^2$ trace identity

Let $p$ be a prime, and let $\text{GL}_n \big( \Bbb{Z} / p^2 \Bbb{Z} \big)$ be the group of $n \times n$ invertible matrices over the ring $\Bbb{Z} / p^2 \Bbb{Z}$. Does there exist a positive integer ...
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### I seem to have them stumped at MSE, what ideal is this? [on hold]

http://math.stackexchange.com/questions/598978/what-ideal-is-this Basically, given an ideal $I$ of $S = R[x_1, \dots, x_n]$, with $R$ a commutative ring, and any set of $n$ polynomials $f_i \in S$, ...
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### Can there be only one (uncountable transitive model of ZFC)?

It is an immediate consequence of Cohen's forcing that if there is one countable transitive model of $\sf ZFC$, then there are many of them. Even if all of these models are of the same height, there ...
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### Determine if a cycle from graph embedded in surface is contractible

Given a graph $G$ embedded in Surface $S$(orientable or non-orientable), and a cycle(a closed walk with no repeated vertex) $C$ from $G$, how to determine if $C$ is contractible based on the rotation ...
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### Probability density function in embedded space

I have a 1D noisy time series X which has a probability density function (pdf) of p(X)=$d*r^{(d-1)}$. Q1 - If I embed X into $d$ dimensional higher space using Attractor reconstruction into $U$ then ...
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### A counting problem

Given $m>1$, what is the number of $2m\times 2m$ matrices, made of $0$ and $1$, such that each row has exactly $m$ ones, and each column has exactly $m$ zeros. I am not sure if this is a ...
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### What is the importance of Noetherian Rings? [on hold]

I know they are important in abstract algebra, but why do people study them? Why are they so important to study? Do they make certain things easier to understand?
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### Verlinde's formula

"Verlinde's formula" predicts the dimension of the space of conformal blocks of a chiral CFT. Depending on... • which chiral CFT one considers (does one restrict to WZW models, or not?) ...
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### Arrangement of N type of objects in a circle [on hold]

There are $N$ types of objects. We can an infinite supply of each type. There are $R$ bins. We can only put one or no object of a particular type in a bin. Now if the bins were arranged in a line, we ...
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### the regular part of Green funtion and its critical points! [on hold]

we all know the existenceness of green funtion for some regular domain.but what technique can we use to study the regular part of green funtion,that is, Robin funtion,especially about its critical ...
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### runs of consecutive non squarefree integers

This question gained no attention at Math SE. Call a sequence of $k$ consecutive naturals squary if each one of them is divided by a square > 1. The Chinese Remainder theorem trivially guarantees us ...
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### Problems for Christmas party [on hold]

We already have wonderful Math puzzles for dinner. But for Christmas parties we can try to make a collection of soft and funny problems accessible not only for mathematicians. Just to start a list... ...
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### An invariant number of modules over Auslander Gorenstein modules

Given an Auslander Gorenstein $R$ of injective dimension $\mu$, one can associate with each finitely generated module $M$ with a number $\varepsilon_{\mu}(M)$, which is the number of the ...
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### question for 'Lectures on Moduli of Curves'

I'm reading Gieseker's Lectures on Moduli of Curves, and I have a question concerning a statement made on page 69. We are given a family $p : Z \to U$ of connected curves of genus $g\geq 2$ and ...
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### functor from semiorthogonal decomposition

Suppose we are given two smooth projective varieties $X$ and $Y$. We consider the derived categories $D^b(X)$ and $D^b(Y)$ of coherent shaeves. Suppose furthermore we are given semiorthogonal ...
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### Examples of non-projective morphisms with projective fibres

Let $X\to S$ be a morphism of noetherian schemes such that, for all $s$ in $S$, the morphism $X_s\to$ Spec $k(s)$ is projective. Then it doesn't follow that $X\to S$ is projective in general. In ...
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### 0-dimensional Gorenstein local ring.

Assume the following condition for the ring T = F_p[[X,S]]/I: Condition 1. T is NOT a zero ring. Condition 2. I is generated by 3 elements of F_p[[X,S]], but NOT by 2 elements. Then, is T a ...
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### Techniques to solve integral [on hold]

What is the process of finding the value of the integral: The limit of the integral is from 0 to Pi/4; the integrand is square root of (3tan^2(x)-1)
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### Binary search with maximum consecutive lies about “is X in subset S?”

Here's the original problem: Alice tells Bob "I have thought of an integer between 1 and 2000. Tell me 1000 numbers. If your set contains my number, I'll give you this prize." Bob really wants ...
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### differences between character distributions of supercuspidal representations and others

Let $G$ be a p-adic linear reductive group. For a irreducible admissible smooth representation $\pi$ of $G$, there is a distribution $\Theta(\pi)$, called the character distribution, attached to ...
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### How to prove a certain connection between the list-chromatic number of a bipartite graph and a cardinal?

Let $G=(L,R,E)$ be a complete bipartite graph, such that $|L|=\aleph_0$ and $|R|=\kappa$. I'd like to show that if $\kappa<2^{\aleph_0}$ then the list-chromatic number of $G$ can't be more than ...
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### Circular Permutations With Repetitions (Mirrored Ignored) [migrated]

For Circular Permutations with unique elements (mirrored ignored) the answer is (n - 1)!/2 (pretty straight forward). However I cant seem to figure out how to calculate circular permutations with ...
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### Has the Ramified Theory of Types been applied to Predicative Set Theories?

Questions of predicativity are well-studied in the context of arithmetic. We have a base theory, first-order Peano arithmetic. Some people, like Edward Nelson and Charles Parsons, consider it to be ...
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### What kind of probability distribution maximizes the average distance between two points?

If $f$ is a probability distribution on the unit disk in $\mathbb{R}^2$, and $X_1$ and $X_2$ are two independent samples from $f$, then what is the distribution $f^*$ that maximizes the average ...
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### Periodic orbits of a spinning ball in a square

Periodic orbits of a billiard ball bouncing in a square have been well-studied. I am seeking similar analysis of what is sometimes called a rough ball, one whose high friction causes it to pick up ...
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### A Product Related to Partitions with Largest Part n

This is a finite version of a problem of mine entitled "A product related to unrestricted partition." It has the advantage that, at least for small values of n, it is easily solved. Begin with the ...
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### Did Godel prove that the Ramified Theory of Types collapses at $\omega_1$?

Second-Order Arithmetic is considered impredicative, because the comprehension scheme allows formulas with bound second-order variables that range over all sets of natural numbers, including the set ...
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### “Pseudo-random” subsets of additive bases

We say that a subset $B \subset \mathbb{N}$ is an (asymptotic) additive basis of order $k$ if the set $kB = B + \cdots + B = \mathbb{N} \setminus C$, where $C$ is a finite set of positive integers. ...
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### Mersenne almost primes

I asked earlier whether it can be proved that infinitely many elements of $P_n$ for some positive value of $n$ (here $P_n$ refers to the set of numbers with at most $n$ prime divisors). There I ...
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### A function composed with itself produces the identity

Let $B$ be the closed unit ball in $\mathbb R^3$ and $f: B\to B$ continuous, such that $f\circ f$ is the identity (i.e., $f\circ f=\mathbb 1_B$) and $f$ restricted on $\partial B$ is also the identity ...
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### How to construct a group with specified growth function

Are there any procedures which given a nonnegative nondecreasing function on the integers will construct a finitely generated group with the same growth up to the usual equivalence of growth ...
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### Status of the $x^2 + 1$ problem

It is a long-standing conjecture (probably just as old as the twin prime conjecture, which has gotten a lot of attention as of late since Zhang and Maynard's breakthrough results this year) that ...
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### The finest countably generated free topological group so that $x^{m_{n}}_n\rightarrow 1$?

What is the finest free topological group $H$ with generators ${x_{1},x_{2},...}$ so that $x^{m_{n}}_n\rightarrow 1$ for all sequences $m_{1},m_{2},...$? Is $H \simeq K$, with $K$ the natural ...
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### why algebraic numbers are periods?

In Kontsevich and Zagier paper, they define a period as a complex number that can be expressed as an integral of algebraic function over an algebraic domain. Then how do we show that all algebraic ...
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### One equation satisfied by Another equation [on hold]

I have small question regarding differential equations. I know it is possible to construct any equation if x and f(x) are given. say (1,1494) then (2,1942) and (3,2578) it is possible with these 3 ...
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### analytic continuation of a function [on hold]

let $f(z)=\sum_{n\ge0}a_nz^n$ be a power series (in $\mathbb C$) with convergence radius $r<\infty$. One assumes that $f(z)$ can be analytically extented in a holomorphic function on $\mathbb C$. ...
$\def\RiemInt{\,\text{-}\,\lower.5mm\hbox{$^{^{\rm Riem}}$}\kern-1mm\int}$ This is essentially a reformulation of this MSE question which has not received any answers for about three weeks. To ...
Suppose $t_n$ is a positive integer sequence with first order asymptotic approximation $t_n$ ~ $2.53^n$. The associated OGF $$T(z)=\sum_{n\geq 0} t_n z^n$$ satisfies ...