## Non averaging sequences in finite groups

Let us say that a non averaging sequence in a group G is a sequence x1,…,xn such that x2i≠xjxk for any indices i,j,k such that two at least are distinct. My question is: given n, what is the smallest group having a non-averaging sequence of length n? Has this question been already tackled in the … Read more

## Convergence of a particular double sum [closed]

Closed. This question needs details or clarity. It is not currently accepting answers. Want to improve this question? Add details and clarify the problem by editing this post. Closed 6 years ago. Improve this question Consider the following double sum: Q(n)=1n2n∑i=1n∑j=1[∂ijlnf(x)]2 where ∂ij is the partial second order derivative (bounded for all indices), the function … Read more

## Table of LCM’s vs. table of products

In 2004 Kevin Ford established sharp asymptotics on Erdős’ problem on the number of different products a⋅b, a,b∈{1,…,n}. (http://arxiv.org/abs/math/0401223, see also discussion here: Number of elements in the set {1,⋯,n}⋅{1,⋯,n}) My naive question is whether there are much less different numbers of the form lcm(a,b), where a,b∈{1,…,n}. Answer AttributionSource : Link , Question Author : … Read more

## Adams Spectral sequence and Pontrjagin-Thom construction [Reference request]

I will be grateful for any reference for the following statements/claims. 1) Let’s consider the case of $p=2$ and the classic Adams spectral sequence with the $E_2$-term given by $\mathrm{Ext}_{A}(\mathbb{F}_2,\mathbb{F}_2)$. If $\alpha$ and $\beta$ are two permanent cycles in the Adams spectral sequence, converging to elements $f\in{_2\pi_i^s}$ and $g\in{_2\pi_j^s}$, then is it true that $\alpha\beta$ … Read more

## Centers of Noetherian Algebras and K-theory

I’ll start off a little vauge: Let E be a noncommutative ring which is finitely generated over its noetherian center Z. Denote by modE the category of finitely generated left E-modules and similarly for modZ. We have a functor F:modZ→modE which takes M to E⊗ZM, hence an induced map on (Quillen) K1-groups K1(F):K1(modZ)→K1(modE). I’m interested … Read more

## Normal fields of geodesic spheres

This question is related to this one (https://math.stackexchange.com/questions/1383511/normal-curvature-of-geodesic-spheres) I’ve asked at math.stackexchange. Let (M,g) be a compact Riemannian manifold with no conjugate points and (˜M,˜g) its universal covering. Let ˆg the Sasaki metric on TM−{0} and dˆg its associated distance function. Fix ˜p∈˜M and R=1. Let ˜H:=˜M−¯B1(p). For x∈˜H, consider the geodesic sphere centered at … Read more

## Natural transformations of A∞A_\infty-functors (between dg-categories) are “directed homotopies” (reference?)

Let A and B be dg-categories over a field, viewed as A∞-categories. The A∞-category (actually, dg-category) of strictly unital A∞-functors A→B will be denoted by Fun∞(A,B). It is described explicitly (in the non-unital case) for example in P. Seidel’s book (“Fukaya category and Picard-Lefschetz theory”). Let Δ1 be the 1-simplex category, namely, the linear category … Read more