**-1**

votes

**0**answers

13 views

### Average, sum … as operator

Is there any 'generalized' name for operators: sum, average and so on (discrete space). Maybe a discrete operator? What is precisely the definition?

**0**

votes

**0**answers

10 views

### State of the art in the expected length of the Longest Increasing Subsequence of a random permutation

I have been reading about the topic motivated by a problem I read that asked for the first three digits of the sum of the LIS lengths in all permutations of length $n$. It is easy to see that we are ...

**2**

votes

**1**answer

32 views

### Ramification of prime ideal in Kummer extension

Let $\mu \in \mathbb{Q}(\zeta_n)$ lie above the rational prime $p$, and let the prime ideal $\mathscr{P}\subset \mathbb{Z}[\zeta_n]$ have ramification index $a$ over $\mu$.
Why is it then true that ...

**0**

votes

**0**answers

32 views

### Fundamental solution of Discrete Laplace in the plane

We consider a discretization of the Laplace operator on $\mathbb Z^2$, https://en.wikipedia.org/wiki/Discrete_Laplace_operator
Then, it is natural to consider its fundamental solution $u$, i.e. ...

**1**

vote

**0**answers

28 views

### On tangent space of relative quot scheme in positive characteristic

Let $k$ be an algebraically closed field of positive characteristic and $f:X \to S$ be a smooth, flat, projective morphism between noetherian $k$-schemes. Assume that $S$ is a non-singular ...

**0**

votes

**0**answers

24 views

### Bounding $\dfrac{r(x)}{\pi(x+r(x))-\pi(x-r(x))}$ with $1\ll r(x)\ll \log^{4}(x)$

I would like to know whether it is possible to obtain the bounds $\sqrt{r(x)}\ll k(x)\ll r(x)$ where $k(x)={\pi(x+r(x))-\pi(x-r(x))}$ and $1\ll r(x)\ll \log^{4}(x)$ and thus ...

**5**

votes

**1**answer

54 views

### Gauge field quantization, electromagnetism

Classical electromagnetism (with no sources) follows from the actions$$S = \int d^4x\left(-{1\over4}F_{\mu\nu}F^{\mu\nu}\right),\text{ where }F_{\mu\nu} = \partial_\mu A_\nu - \partial_\nu A_\mu.$$The ...

**1**

vote

**0**answers

60 views

### Homogeneous polynomials on $\mathbb{P}^5$ which vanish on $\mathbb{P}^2$

I have the following questions, both of which has been claimed/used in Fulton and Harris's Representation Theory book.
Suppose $\mathbb{P}^2$ sits inside $\mathbb{P}^5$ via the Veronese map (both are ...

**1**

vote

**1**answer

35 views

### Orbits in the adjoint representation of $SU(2,1)$

How can one describe the orbits of the Lie group $G=\mathrm{SU}(2,1)$ in its Lie algebra $\mathfrak{g}=\mathfrak{su}(2,1)$ with respect to the adjoint representation?

**2**

votes

**2**answers

112 views

### Which journals publish short notes in discrete mathematics?

The journal Discrete Mathematics contains a lot of short notes (i.e., less than 7 journal pages). What are some other journals that publish short notes in discrete mathematics? I've looked at other ...

**0**

votes

**0**answers

31 views

### Which Dihedral Groups are $CI$-Groups?

Let $D_{n}$ denotes the dihedral group of order $2n$. Firstly, for self-referencing of the question, I give some definitions which are standard.
Let $G$ be a finite group. A subset $S$ of group $G$ ...

**4**

votes

**0**answers

28 views

### 6j symbols of SU(4) at level 4

Does anybody know of a reference that gives the (quantum) 6j symbols of SU(4) at level 4?
Alternatively, I know the S-matrix and the fusion rules, in the form
$a \times b = \sum_i N^{ab}_{c_i} c_i$
...

**4**

votes

**0**answers

45 views

### Zeros of eigenforms at a given elliptic curve

Let $N$ be an integer, let $\Gamma(N) \subseteq \textrm{SL}_2(\mathbb Z)$ be the kernel of reduction modulo $N$ and $s \in X(N)(\mathbb C) = \Gamma(N) \backslash \mathbb H^*$, then one can define ...

**8**

votes

**0**answers

77 views

### Tiling a square with rectangles

Is it possible to completely tile a square with different rectangles of integer sides but all with the same area?
The original problem, not requiring integer sides for rectangles, was proposed by Joe ...

**0**

votes

**0**answers

23 views

### “4th order” floretions- cyclic transformation question

In response to the last paragraph mentioning "swapping" operations in this post, I would like to mention what the reference is to and one question I currently have.
Assume $X = abCD$ is some 4th ...

**0**

votes

**0**answers

11 views

### Maximum subgraph edge distance greater than given number

I have a weighted graph G with approximately 75000 nodes. I would like to find subgraph G' induced on a subset of nodes, such that all edge weights in G' are greater than a given constant C and the ...

**2**

votes

**2**answers

217 views

### Primes $p$ for which $2p-1$ is prime

It's a well-known open problem (Sophie-Germain primes) whether there are infinitely many primes $p$, $2p+1$. What about $p$, $2p-1$?
Seemingly it's also an open problem (see here and the linked ...

**5**

votes

**0**answers

103 views

### Descent theorems for fundamental groups and groupoids?

Grothendieck in his 1984 "Esquisse d'un programme" (Section 2) wrote (English translation):
" ..,people still obstinately persist, when calculating with fundamental groups, in fixing a single base ...

**-1**

votes

**0**answers

35 views

### Random walk on weighted graph

Suppose we have an undirected and weighted graph $G$, a random walker move from node $i$ to node $j$ with $P(i,j)= w_{ij} / d(i)$. Now suppose we have integer $w$ set that is $w= \{ 1,2,..\}$, my ...

**1**

vote

**0**answers

27 views

### The characteristic polynomial of the product of two linear recurrences

Let $\mathbb{F}$ be a field and let $(a_n)_{n \geq 0}$, $(b_n)_{n \geq 0}$ be two linear recurrences with terms in $\mathbb{F}$ and respective characteristic polynomials $f(X), g(X) \in ...

**3**

votes

**1**answer

134 views

### Is $2^n -1$ finitely many times the product of consecutive primes? [duplicate]

This question was asked at MSE but recieved no attention at all.
Here it is:
Are there finitely many $(n,k) \in \mathbb{N}^2$ with $2^n-1=p_1p_2\cdots p_k$ ?
$p_1=3,p_2=5 , ...,p_k$ are ...

**4**

votes

**0**answers

49 views

### positions of polyhedrons with vertices on the unit sphere

Let $S^2$ be the unit $2$-sphere canonically embedded in $\mathbb{R}^3$. Let $P$ be a polyhedron whose all vertices are in $S^2$. Let $\text{Iso}(S^2)$ be the isometry group of $S^2$ and ...

**3**

votes

**1**answer

50 views

### Conditions on the hierarchy for Thurston's hyperbolization theorem

From my understanding the proof of Thurston's hyperbolization theorem for Haken $3$--manifolds consists of cutting the manifold along a hierarchy (collection of incompressible, ...

**1**

vote

**0**answers

22 views

### Geodesically convex neighborhood in Finsler manifolds

It is well known that every point of a Riemannian manifold $(M,g)$ possesses a fundamental system $\{U_n\}_{n\in\mathbb N}$ of geodesically convex neighborhoods. This means that every pair of points ...

**8**

votes

**0**answers

58 views

### Idea behind the proof of consistency of club filter of $\omega_1$ is ultrafilter + ZF + DC

I've been trying to understand Radin Forcing and some of its applications, one of which is the use of it to prove the consistency of ''Club filter of $\omega_1$ is an ultrafilter + ZF + DC''. However, ...

**0**

votes

**0**answers

13 views

### Hilbert transform on boundary value of analytic bounded functions

I am considering the boundary values of a bounded holomorphic functions. Suppose $w$ is a bounded holomorphic function in upper half plane, with continuous and bounded boundary value $f$ on real axis. ...

**-5**

votes

**0**answers

75 views

### Infinite sum of n from 1 to infinity tend to -1/12 in String Theory? [on hold]

Why is this wrong result:
$$
\sum\limits_{n=1}^{\infty}n\rightarrow-\frac{1}{12}
$$
Used here: Volume I - String Theory - Joseph Polchinsky
Can someone explain its meaning in this book?
EDIT
I ...

**2**

votes

**1**answer

33 views

### Proving compatibility of two Partial differential equations

Given two PDE(s): $F(x,y,z,p,q)=0$
and $G(x,y,z,p,q)=0$
In I.A.N Sneddon's "Elements of Partial Differential Equations",If every solution of $F=0$ is a solution of ...

**4**

votes

**1**answer

99 views

### Another question on Heath-Brown's “Prime twins and Siegel zeros”

With a graduate student, I'm going through the paper (Proc. London Math. Soc. (3) 47 (1983), no. 2, 193–224.)
Here's the background and notation.
We have a quadratic character $\chi$ modulo $q$, ...

**3**

votes

**0**answers

64 views

### Enriching categories and equivalences

Let $\mathcal{C}$ and $\mathcal{D}$ be two equivalent categories. Furthermore, assume $\mathcal{C}$ is enriched over a monoidal category $(\mathcal{M}, \otimes)$. Can one use the equivalence to ...

**2**

votes

**0**answers

33 views

### Conditions on the fusion data of symmetric fusion category

We know that every symmetric fusion category (SFC) gives rise to data
$N^{ij}_k$ that describe the fusion of simple objects:
$i\times j = N^{ij}_k k$, and the data $\theta_i =\pm 1$ that describe the ...

**5**

votes

**1**answer

90 views

### History of spectral methods to the study of real analytic $GL_2$-Eisenstein series

I'm trying to sort out the history of spectral methods in the study of real analytic $GL_2$-Eisenstein series. From what I read so far, I would say that the subject was really kicked off by the ...

**2**

votes

**1**answer

142 views

### Polynomial differential forms on $BG$

Let $\Omega^{*}_{\text{poly}}\: : \: sSet\to dg_{\geq 0}Comm_{+}$ be the polynomial De Rahm functor on simplicial sets, where the codomain is the category of commutative differential graded algebras ...

**-1**

votes

**0**answers

52 views

### free quotient in Limit groups [on hold]

Let G a limit group.
Exist N normal subgroup not trivial of G such that G/N is a free group finitely generated and d(G)=d(G/N)?, where d() is the minimum number of generators of G.

**-3**

votes

**0**answers

37 views

### Perfect matching in a graph [on hold]

Is it true, that in every 2-regular graph with 14 vertices there is a perfect matching ? If you think it's true - prove it, otherwise show counter-example
this is my excercise. I think that it's true ...

**0**

votes

**0**answers

28 views

### Stability of moment representation of a scalar real-valued function

Let $f \in C([0,1],\mathbb R)$ be a continuous function. Define the moments of $f$ by
\begin{align*}
m_i(f) := \int_0^1 x^i f(x) dx,
\end{align*}
which yields a sequence of real numbers.
Now given ...

**-5**

votes

**0**answers

24 views

### Finding equivalent matrix combination [on hold]

I have a program I've written that is solving some problems with some matrix-vector math, but I have a feature I want to add and while I've found a work around an analytic solution would be superior. ...

**-2**

votes

**0**answers

125 views

### Smoothness and Cohen Macaulay

One always get the idea (almost a slogan in Alg. Geom.) that Cohen-Macaulay varieties will have some (mild) singularities and Gorenstein can be smooth.
I found a smooth scheme that by construction ...

**0**

votes

**0**answers

15 views

### Interpolation with double second differences [on hold]

My question is about an interpolation method used in an astronomy book that I would like to understand, and that can be found here: ...

**-5**

votes

**0**answers

38 views

### mutual information problem [on hold]

In mutual information we have: if $x$ and $y$ are independent then
$p(x,y)=p(x)p(y)$ and then $I(X;Y)=0$.
Do If $I (X;Y) = 0$ when $x$ and $y$ are independent?

**-6**

votes

**0**answers

42 views

**3**

votes

**0**answers

76 views

### When does a “universal” quot scheme exist?

Suppose $M$ is a moduli space of semistable sheaves on a projective variety $X$. Let $v$ be some the discrete invariants. I would like to form a space $\mathcal Q(v) \rightarrow M$, where the fiber ...

**0**

votes

**0**answers

26 views

### Existence and summability of cumulant [on hold]

I posted this question on math stackexchange, but no one answered. So I am seeking help here.
1) Is the statement "the $r$-th order moment exists" equivalent to "the $r$-th order cumulant exists"? ...

**-5**

votes

**0**answers

22 views

### mutual information entropy problem [on hold]

In mutual information we have: if $x$ and $y$ are independent then
$p(x,y)=p(x)p(y)$ and then $I(X;Y)=0$.
Do If $Y (X;Y) = 0$ when $x$ and $y$ are not necessarily independent?

**2**

votes

**1**answer

170 views

### Doob Martingale: Where is the catch?

I am working on a research problem in uncertainty propagation that involves sums of possibly dependent random variables with bounded sets of support.
I am attempting to use the method of bounded ...

**1**

vote

**1**answer

76 views

### Questions on topologies on space of Radon measures

Consider the space $C_c(\mathbb{R})$ of continuous real-valued functions on $\mathbb{R}$ equipped with the inductive limit topology by $C_c(\mathbb{R}) = \bigcup_{n \in \mathbb{N}} C_c(\mathbb{R}, ...

**0**

votes

**0**answers

25 views

### Discrete random walk with uniformly distributed transition p, set initially

I've been working on a discrete version of the "unreliable friend" distribution. It would seem that what I've come up with is equivalent to the following random walk:
Choose $p$ from $U(0,1)$
Start ...

**0**

votes

**0**answers

53 views

### Is there any $ABCDS$ pyramid (where $ABCD$ is a rectangle) in which each 2 edges have different lengths and $|AS|+|CS|=|BS|+|DS|$? [on hold]

I had geometry quite a while ago and I wonder if anyone has any idea how to tackle this problem:
Is there any $ABCDS$ pyramid (where $ABCD$ is a rectangle) in which each 2 edges (except for the base) ...

**0**

votes

**0**answers

20 views

### Variant of (WEAK) PARTITION with 2 distinct solutions [on hold]

I am interested in the complexity of the following problem:
Input: A list $a1\leq ⋯ \leq a_n$ of positive integers.
Question: Are there two vectors $x, x'\in\{−1,0,1\}^n$ such that
...

**3**

votes

**1**answer

59 views

### Spin Structures for Quaternionic-Kaehler and Hyper-Kaehler Manifolds

As is well-known (see Friedrich's book for example) every Kähler manifold is spin (or at least spin$^c$) and the Dirac is given (up to a twist) by $\partial + \partial^*$. What happens in the ...