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: 1 hour ago

Math

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: $\binom{N+i}{i} x =0 \quad .... Victoria: 1 hour ago Math Is total variation distance of normalized sum of random variables to Gaussian monotonic decreasing? Let$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: 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: 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: 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$1653$-simplices. .... 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: 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: 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: 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: 6 hours ago