Math questions and answers

Math

When two determinantal ideals together generate a power of the maximal ideal?

(A somewhat technical question, but maybe it is well known.) Consider matrices over the ring $k]$, whose entries vanish at the origin (i.e. belong to the maximal ideal $\mathfrak{m}$). Denote by $J(A_{k,l})$ the ideal of maximal minors of the matrix $A_{k,l}\in Mat(k,l,\mathfrak{m})$. Given two generic enough (and mutually generic!) matrices, ....

Anthony Anthony: 1 hour ago

Math

Computational solutions to families of systems of linear equations

Question Does there exist a computer package that will solve families of systems of linear equations over a field of prime characteristic? An Example Suppose I wanted to know when the following system of equations had a non-zero solution x over a field of characteristic p: $\binom{N+i}{i} x =0 \quad ....

Victoria Victoria: 1 hour ago

Math

Is total variation distance of normalized sum of random variables to Gaussian monotonic decreasing?

Let $X_1, X_2, \ldots$ be independent and identically distributed random variables with mean $0$ and variance $1$ and let $S_n = (X_1 + \cdots + X_n)/\sqrt{n}$ to be their normalized sum. Define $D_n$ to the total variation (TV) distance between $S_n$ and a standard Gaussian. Question: Is $D_n$ always monotonic ....

Daniel Daniel: 2 hours ago

Math

What is an example of a smooth variety over a finite field F_p which does not lift to Z_p?

Somebody answered this question instead of the question here (https://mathoverflow.net/questions/410/what-is-an-example-of-a-smooth-variety-over-a-finite-field-fp-which-does-not-emb), so I am asking this with the hope that they will cut and paste their solution. ....

Savannah Savannah: 2 hours ago

Math

About the prime divisors of values of polynomials

Let $P$ be a polynomial having integer coefficients (and degree $\geq 3$), and let $\mathscr P_P$ be the set of prime numbers dividing some value $P(n)$ with $n \in \mathbb Z$. Is it true that $\sum_{p \in \mathscr P_P} \frac1 p$ diverges? The case of polynomials with degree $2$ can ....

Nova Nova: 3 hours ago

Math

Seeking very regular $\mathbb Q$-acyclic complexes

This question was raised from a project with Nati Linial and Yuval Peled We are seeking a $3$-dimensional simplicial complex $K$ on $12$ vertices with the following properties a) $K$ has a complete $2$-dimensional skeleton (namely, every triple of vertices form a 2-face of $K$) and it has $165$ $3$-simplices. ....

Isabella Isabella: 4 hours ago

Math

Berry–Esseen bound for operator norm of matrix averages

Is there a Berry–Esseen bound for operator norm of an average of independent random matrices? Suppose $A_1, \dotsc, A_n$ are independent matrices with $\mathbb{E} = I$ (the identity matrix). Is there a Berry–Esseen bound for properly normalized $\lVert\overline{A} - I\rVert_\text{op}$? ....

Addison Addison: 5 hours ago

Math

A variant of Turán–Kubilius inequality

Let $\omega(n)$ the number of distinct prime factors of $n$ (counted without multiplicity). A famous consequence of Turán–Kubilius inequality is $$ \sum_{n\leq x}(\omega(n)-\log\log x)^2=O(x\log \log x). $$ However, I am interested in a small variation of the previous result. Indeed, I would like to obtain a similar result to $$ ....

Sadie Sadie: 5 hours ago

Math

Finding the Levy triplet of a Levy process

I know the levy triplet of a Poisson process $N_t$- $(0,0,\lambda\delta_{1}(y))$ and its characteristic function is $\phi_N=exp$ and also that of the standard $\alpha$ stable subordinator $D_t$ - $(\frac{iu\alpha}{\Gamma(1-\alpha)},0,\frac{\alpha}{\Gamma(1-\alpha)}y^{-\alpha-1}dy)$ and its characteristic function is $\phi_{D}(u)=exp$ My question is how do I find the triplet of $(N_t,D_t)$ where $N_t$ and $D_t$ ....

Emma Emma: 5 hours ago

Math

Low-dimensional irreducible 2-modular representations of the symmetric group

I apologize if this question is a little too basic for MathOverflow, but it's somewhat outside of my background and I'm frustrated that the answer doesn't seem to be explicit in the literature even though I suspect it's easily known by the experts. What are the lowest-dimensional irreducible representations over ....

Leilani Leilani: 6 hours ago