# All Questions

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### Elementary question of Group cohomology

Let $G$ be a finite group. Assume $G$ acts on finite abelian module $M$ such that $(|G|,|M|)=1$. Question: Why $H^i(G,M) = 0$ for $i > 0$? Pierre MATSUMI
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### Relationship of ${\cal P}(\omega)/fin$ and ${\cal L}$

Define ${\cal L}$ as in this question: the set of functions $f:\mathbb{N}\rightarrow\mathbb{N}$ such that $f(n)\leq f(n+1)\leq f(n)+1$, where two functions are considered equal if they differ at at ...
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### Flower Arrangements [on hold]

We have a $n\times m$ grid with $k$ flowers (not necessarily distinct). The grid is assumed to have horizontal and vertical symmetry. What is the value of $A(n,m,k)$, where $A(n,m,k)$ is the number of ...
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### Solve the recurrence formula $a_{n+1} = 2 a_n + 1/a_n$ with $a_1 = 1$ [on hold]

How to solve for general term of $a_{n+1} = 2 a_n + 1/a_n$ with $a_1 = 1$ Thanks in advance!
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### Brouwer's theorem for the Cauchy reals

Brouwer famously proved, using principles motivated by intuitionistic choice sequences, that every function $\mathbb{R}\to \mathbb{R}$ is continuous. In Sheaves in geometry and logic (section VI.9), ...
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I have a system of $n$ congruences. the generic $m$_th congruence of the system ($m = 1,\dots,n$) is in the form: $(p_n\#)^2(\displaystyle\sum_{\substack{i=1\\i\neq ... 0answers 36 views ### Differentiability of the function$\frac{x}{1+\|x\|}$[on hold] Is the function$f:\mathbb{R}^n\to\mathbb{R}$given by $$f(x)=\frac{x}{1+\|x\|},\;\;\forall x\in \mathbb{R}^n,$$ where$\|x\|=\sqrt[]{\sum_{i=1}^n{x_i}^2}$,, for all$x=(x_1, x_2,...x_n)$in ... 0answers 62 views ### A “universally non Hypercomplete”$\infty$-topos? My question is : Is there a classifying$\infty$-topos for$\infty$-connected objects ? Does this$\infty$-topos has a nice description (as an$\infty$-category ) ? What I mean by$\infty$-connected ... 0answers 80 views ### Rings that are$K_0$of finite groups Is there a simple characterisation of all rings which appear as$K_0$of finite groups? By$K_0$of a finite group$G$I mean$K_0(\mathbb C[G])$which in the same as a ring of virtual characters of ... 0answers 143 views ### Is an irreducible ideal in$R$also irreducible in$R[x]$? Let$R$be a commutative Noetherian ring and$I\subset R$an ideal that is irreducible in the sense that if$I = J_1 \cap J_2$, then$I=J_1$or$I=J_2$. Is (the ideal generated by)$I$irreducible in ... 0answers 90 views ### Does the Bombieri-Lang conjecture imply severe restrictions on rational points on twists of hyperelliptic curves? According to Silverman, the Bombieri-Lang conjecture implies that the rational points of surface on general type lie on finite set of curves, except for a finite set of points. Let$f$be univariate ... 0answers 63 views ### Non-standard numbers and exponential form of Zeta function Basic idea For a long time I was looking for a numerical system that would allow to compare infinite sets. In contrast to Cantor's approach that empathizes the possibility of on-to-one correspondence ... 0answers 42 views ### Are all derivatives of sinc function bounded on real axis? [on hold] It seems that all derivatives of sinc function (sinc(x)=sin(x)/x) are bounded on real axis. Is it true or no? Thanks in advance. 1answer 43 views ### Does order-preserving equal continuous? [on hold] Let$P,Q$be posets and endow them with the interval topology$\tau_i(P)$and$\tau_i(Q)$respectively. Is it true that if$f: P\to Q$is order-preserving, then it is continuous, and vice versa? 0answers 26 views ### Path-connected Hausdorff interval topologies Let$(P,\leq)$be a poset with more than$1$point such that the interval topology$\tau_i(P)$is path-connected and$T_2$. Does this imply that$[0,1]$order-embeds into$P$? (This is a follow-up ... 0answers 32 views ### Minkowski spacetime in Newman Penrose formalism I have a rather basic question for which (surprisingly!) I cannot find a short and clear answer anywhere: I'm currently looking at the Newman Penrose (NP) formalism (I use primarily Chandrasekhar's ... 0answers 92 views ### Indecomposable representations of a wreath product If$G$is a finite group, we know the irreducible representations of$G ≀ S_n$(over$\mathbb Q$) are classified by partitions of$n$'decorated' by an irrep of$G$. I'm wondering to what extent the ... 0answers 53 views ### “Edge Density” of Infinite Planar Graphs Given an infinite planar graph$G$, let's denote by$\{H_1,H_2,\dots,H_m\}$all the labeled graphs on$n$vertices that appear as subgraphs of$G$. Also let $$d_n=\frac{\sum_{i=1}^m \#E(H_i)}{nm}$$ ... 0answers 87 views ### Elementary examples on sheaf extension Let$V\subset\mathbb{P}^n$be a projective variety and$C_V$its conormal subvariety in$T^\ast\mathbb{P}^n$. Denote by$\mathscr{O}_{C_V}$its structure sheaf, then when will the condition ... 0answers 66 views ### Representing rational homotopy class by geometric objects Given a smooth manifold$M$, we can study its rational homotopy type by looking at differential forms. I am wondering if there is a way to represent each$rational$homotopy class by geometric ... 1answer 54 views ### convex hull of the set of permutations with one cycle is there a way to describe the convex hull of the set of permutation matrices with exactly one non-trivial cycle? or maybe I should ask for the convex hull of cycle matrices : let$(i_{1},..,i_{k})$... 1answer 90 views ### Kernel of the natural map between group$C^*$-algebras Let$\Gamma$be a discrete group. We can form two$C^*$-algebras: the universal (or full) and reduced, to be denoted by$C^*_u(\Gamma)$and$C^*_r(\Gamma)$(respectively). Both of them are completions ... 2answers 699 views ### Why should we care about “higher infinities” outside of set theory? Let's say you are a prospective mathematician with some addled ideas about cardinality. If you assumed that the natural numbers were finite, you'd quickly vanish in a puff of logic. :) If you ... 2answers 342 views ### Geodesics on SO(3) I have two 3D rotations about the origin, represented as$3 \times 3$orthogonal matrices$M_1$and$M_2$(specified by numerical entries), and I would like to interpolate (and compute) a continuous ... 0answers 32 views ### C^1 Sard related question Let$X$be a$k+1$rectifiable set with finite$k+1$Hausdorff measure in$\mathbb{R}^{n+1}$and set$Z=\{x\in X;\;\ \textrm{s.t} \;\; e_{n+1}\perp T_xX \}$, where$T_xX$is the approximate tangent ... 0answers 31 views ### Coupling Marginals of Distributions on the Sphere Given a distribution$P_X$on$\mathbb{R}$, when does there exist a coupling (i.e. joint distribution)$P_{X^n}$of$X_1,...,X_n$, each distributed according to$P_X$, such that$\sum X_i^2 = n$... 0answers 52 views ### Listing all Lattice Points in a Box Let$B := [-1,1]^n$be an$n$-dimensional box. Moreover, let$v_1,\ldots,v_n \in \mathbb{R}^n$form a basis of$\mathbb{R}^n$, where the entries of the$v_i$are explicitly irrational. We can assume ... 0answers 28 views ### About the partial expectation polynomials in the Interlacing-I paper and perfect matchings I am thinking of the polynomials$f_{s_1,s_2,..,s_k}\$ as in the definition 4.3 in this paper http://annals.math.princeton.edu/wp-content/uploads/annals-v182-n1-p07-p.pdf In the use of these ...

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