Questions tagged [reference-request]

This tag is used if a reference is needed in a paper or textbook on a specific result.

Filter by
Sorted by
Tagged with
7 votes
1 answer
521 views

Is the definition of Gerstenhaber bracket related to operads?

I was reading these notes by Keller. On the page 19 he defines the Gerstenhaber bracket on the Hochschild cochain complex. But first of all he defines the operation $\bullet$ on the cochains by $$ \...
Sasha Patotski's user avatar
7 votes
1 answer
1k views

What are current trends/questions in algebraic logic?

What are current trends/questions in algebraic logic? I mean the research developed by Paul Halmos. Could anyone give some references for the overview of its history? Any overview of its application ...
XL _At_Here_There's user avatar
7 votes
2 answers
509 views

Recovering a Weighted Graph from Shortest Path Distances

I am interested in the following problem (A) and its related formulation (B). (A) Suppose that $G = (V,E,w)$ is an unknown weighted graph on the vertex set $V$ and that one has access to $d_G(v,v'), \...
Skoro's user avatar
  • 168
7 votes
1 answer
639 views

The Irreducible Corepresentations of the eight-dimensional Kac-Paljutkin Quantum Group

I asked this question on Math.Stack but have not had any answers. Question What are the irreducible corepresentations of the eight-dimensional Kac-Paljutkin Quantum Group, $A$? The trivial ...
JP McCarthy's user avatar
7 votes
2 answers
996 views

For what spaces is the Hardy-Littlewood maximal operator of strong type $(p,p)$ if and only if $p > p_0 > 1$?

(This is essentially a continuation of my previous question, here.) Let $(X,d,\mu)$ be a metric measure space, i.e. $\mu$ is a Borel measure on the metric space $(X,d)$. Further assume (though you ...
user avatar
7 votes
2 answers
1k views

Internal Day convolution

Let me recall that any small category $\mathbb{A}$ enriched in a complete and cocomplete symmetric monoidal closed category $\mathbb{V}$ admits embedding (the Yoneda embedding): $$y_\mathbb{A} \colon \...
Michal R. Przybylek's user avatar
7 votes
1 answer
800 views

Where do the Kähler Identities first appear?

The Kähler identities (sometimes known as the Hodge identities) are an important collection of relationships between operators on the exterior algebra of a Kähler manifold. These relationships ...
Michael Albanese's user avatar
7 votes
1 answer
381 views

Status of the Isomorphism problem for automatic groups?

I only ask because I don't know how to look for the answer.
some guy on the street's user avatar
7 votes
2 answers
577 views

Representation theory of Discrete Subgroups of Lie groups

My question is the following. Which representations of $Sp(2g, \mathbb Z)$ are extendable to representations of $Sp(2g, \mathbb C)$ or $Sp(2g, \mathbb R)$. Is there a general theory and a good ...
Anant Atyam's user avatar
7 votes
1 answer
480 views

Fundamental groups of compact manifolds with non-negative Ricci curvature.

I would like to find an appropriate reference for the following statement: Statement. Let $M$ be a compact Riemannian manifold with non-negative Ricci curvature. Then $\pi_1(M)$ is virtually abelian. ...
aglearner's user avatar
  • 14k
7 votes
1 answer
2k views

Pochhammer symbol of a differential, and hypergeometric polynomials

I have a minor result which I'm sure has come up somewhere before but I can't seem to find it. Consider a confluent hypergeometric function of the form $$\newcommand{\ff}{{}_1F_1} \ff(b+k;b;z)\...
Emilio Pisanty's user avatar
7 votes
1 answer
533 views

GCH+ Kurepa Families

I have a couple of questions about known theorems for GCH+Kurepa families. Definition first: Let $\kappa$ be a infinite cardinal. A $\kappa^+$ Kurepa family is a family $F$ of subsets of $\kappa^+$ ...
Ioannis Souldatos's user avatar
7 votes
1 answer
1k views

The Correlation of the Möbius Function and Dirichlet Characters

Let $\chi$ be a Dirichlet character, and define $\phi_\chi (n)$ so that it satisfies $$\sum_{n=1}^\infty \phi_\chi (n)n^{-s}=\frac{\zeta(s-1)}{L(s,\chi)}.$$ In other words $$\phi_{\chi}(n)=\sum_{d|...
Eric Naslund's user avatar
  • 11.3k
7 votes
1 answer
851 views

Symmetric extensions and class forcing

Suppose $V\models ZFC$ and $P\in V$ is a poset of forcing conditions. It is a basic theorem in forcing that $V[G]\models ZFC$ for any generic extension by a $V$-generic filter $G$. It is also known ...
Asaf Karagila's user avatar
  • 38.1k
7 votes
1 answer
919 views

Groups whose normal subgroups form a chain with respect to inclusion

Let G be a finite group. In general, given two normal subgroups N and K of G, we need not have N < K or K < N. The easiest example is the Klein 4-group V4 and its subgroups of order 2. So assume ...
Amin's user avatar
  • 307
7 votes
1 answer
949 views

Subfactor theory and Hilbert von Neumann Algebras

There seem to be intimate connections between the different definitions of von Neumann module. The two that I'm aware of are Hilbert von Neumann modules and correspondences (in the sense of Connes). I ...
Ollie's user avatar
  • 1,391
7 votes
1 answer
1k views

Character table for the affine group of Z/p^nZ

Initial caveat: the following question could probably be answered by Google, MathSciNet or my library, if I could find the right search terms or book... but I've not had any luck today, so I hope ...
Yemon Choi's user avatar
  • 25.5k
7 votes
1 answer
629 views

Model theory stressing order type of universe.

In Appendix B to their Model Theory, Chang and Keisler list some problems and conjectures that, at the time of publication, were unsolved. A few of them take imperative form, for instance: "Develop a ...
Cole Leahy's user avatar
  • 1,101
7 votes
3 answers
884 views

Generic Noether normalisation

Suppose that $M$ is a finitely generated module over $A=k[X_1,\ldots,X_n]$ of Krull dimension $m$ with $k$ an infinite field. Then one version of Noether normalisation says there is an $m$-dimensional ...
Simon Wadsley's user avatar
7 votes
1 answer
312 views

Literature about formalization of "natural reasoning" in mathematical logic

In "Logic of sheaves of structures", X. Caicedo justifies the logic he introduces stating (more or less) that assertions about a point should really be understood as assertions about a ...
user524506's user avatar
7 votes
1 answer
200 views

Compact objects in slice categories of finitely presentable categories

Given a locally finitely presentable category $\mathscr C$ and an object $X \in \mathscr C$, it is not so hard to show that a morphism $(X \to Y)$ is compact in $\mathscr C_{X/}$ if it can be obtained ...
R. van Dobben de Bruyn's user avatar
7 votes
1 answer
281 views

The origin of a planar graph theorem of Steinitz and Rademacher

The subsequent statements are extracted from the article titled 'Generating r-regular graphs' (https://doi.org/10.1016/S0166-218X(02)00593-0). A well-known classical theorem of Steinitz and ...
L.C. Zhang's user avatar
  • 1,605
7 votes
2 answers
822 views

Positivity of the coefficients of Taylor series associated to the Riemann hypothesis

The question below relates to the paper "Jensen Polynomials for the Riemann Zeta Function and Other Sequences" of Griffin, Ono, Rolen and Zagier. I'm asking it here because I am sure the ...
Jon Bannon's user avatar
  • 6,977
7 votes
1 answer
201 views

Non-recurrent points of $F(a,b)=(b,ba)$ in a compact metric group $G$

Consider a compact metric group $G$ [A compact topological group $G$ where the topology is generated by an invariant metric]. I am particularly interested in the case where $G$ is the $n$-dimensional ...
Saúl Pilatowsky-Cameo's user avatar
7 votes
2 answers
236 views

Congruences of binomial sums

Let $a_n$ is a binomial sum, for example $$ a_n := \sum_{k} \binom{n-k}{k} \quad \text{or} \quad \sum_{k=0}^n\binom{n+k}{n-k}\binom{2k}{k} \quad \text{or} \quad \sum_{k=0}^n\sum_{\ell=0}^k\binom{n}{k}\...
Igor Pak's user avatar
  • 16.3k
7 votes
1 answer
387 views

Combinatorial reciprocity for symmetric functions

I am wondering whether a certain instance of combinatorial reciprocity (in the sense of Stanley's classic paper "Combinatorial Reciprocity Theorems"), concerning symmetric functions, is ...
Sam Hopkins's user avatar
  • 22.7k
7 votes
2 answers
468 views

Finite generation of motivic cohomology of number fields

Let $F$ be a number field ($F=\mathbb Q$ is fine for my purposes) and let $n\geq2$ be an integer. Is it known whether the first motivic cohomology groups $$\mathrm H^1(\mathrm{Spec}(F),\mathbb Z(n))$$ ...
Alexander Betts's user avatar
7 votes
1 answer
460 views

Reinhardt's ultimate classes

In the preface to Sets and Classes by Muller, several research programs are outlined that were in development concurrently with publication (or finished slightly beforehand) that he would have liked ...
Alec Rhea's user avatar
  • 8,977
7 votes
1 answer
326 views

Harmonic functions on complete Riemannian manifolds

I have started reading a paper of Colding and Minicozzi, where they prove that on a complete Riemannian manifold $M$ of non-negative Ricci curvature, the space of harmonic functions of growth order at ...
Sakunee's user avatar
  • 71
7 votes
1 answer
213 views

Invariants for the isotropy representation of a Riemannian symmetric space

Statement: Let $M = G/K$ be a Riemannian symmetric space of compact type, and $V = T_o M$ be its isotropy representation (of $K$ acting on the tangent space of $M$). Then the Hilbert–Poincaré series $...
Gro-Tsen's user avatar
  • 29.9k
7 votes
3 answers
320 views

Best source for classification of right-angled hyperbolic hexagons

A standard fact that underlies the Fenchel-Nielsen coordinates on Teichmuller space is the fact that for all triples $(a,b,c)$ of positive real numbers, there exists a unique hyperbolic hexagon whose ...
Lisa's user avatar
  • 71
7 votes
1 answer
257 views

Stallings' binding tie

I came to know that the statement below could be proved using Stallings' binding tie argument, though I have no reference article proving the statement by the binding tie argument. Can anyone help me ...
Random's user avatar
  • 927
7 votes
1 answer
469 views

Fibonacci embedded in Catalan?

Given a partition $\lambda$ and its Young diagram $\pmb{Y}_{\lambda}$, we say $\lambda$ is a $(t,s)$-core partition provided that neither $t$ nor $s$ is a hook length in $\pmb{Y}_{\lambda}$. We now ...
T. Amdeberhan's user avatar
7 votes
1 answer
657 views

General wedge-product for vector bundle valued forms

In mathematics and physics, especially gauge theory, there are many different but related notions of wedge products when discussing vector space- and vector bundle-valued differential forms. For ...
G. Blaickner's user avatar
  • 1,137
7 votes
1 answer
817 views

Filtered homotopy colimits and singular homology

Suppose I have a functor $$ X_\bullet: I \to \text{Spaces} $$ where $I$ is a small filtered category. It seems to be a "folk theorem" that the homomorphism $$ \underset{\alpha\in I}{\text{...
John Klein's user avatar
  • 18.6k
7 votes
1 answer
255 views

Reference for proof of an integral from the "Tables of Integral Transforms" involving a Gaussian and a Laguerre polynomial

I am looking for a proof of one of the integrals presented in Harry Bateman's Tables of Integral Transforms. The specific integral in question is presented on page 42 in chapter 8.9 as equation (3): $$...
schade96's user avatar
7 votes
2 answers
239 views

What are the "correct" references for the Vassiliev invariant?

Is there a good survey paper which describes the general ideas of Vassiliev's invariant? I am not an expert on knot theory, many references are too technical for me. Could Vassiliev's invariants be ...
user8749's user avatar
7 votes
1 answer
440 views

Formal completion of a quotient stack

$\newcommand{\Rep}{\operatorname{Rep}}$ $\newcommand{\mo}{\operatorname{-mod}}$ $\renewcommand{\hat}{\widehat}$ I apologize in advance if this is a naive question but my background in algebraic ...
Adrien's user avatar
  • 8,234
7 votes
4 answers
357 views

Discretizing a line segment with pixels which satisfies the Pythagorean theorem

There are plenty of line drawing algorithms to discretize line segments using pixels. The Bresenham's algorithm gives a line where the number of pixels in the segment is the same as its width (in x-...
Per Alexandersson's user avatar
7 votes
1 answer
640 views

Taylor expansion with remainder on locally convex spaces

It is usual to introduce Fréchet and Gâteaux derivatives in Banach spaces. In this context, the familiar Taylor expansion with remainder is also at hand, as you can see on the picture below taken from ...
IamWill's user avatar
  • 3,151
7 votes
1 answer
220 views

What is known about the non-existence of strongly regular graphs srg(n,k,0,2)?

Only few strongly regular graphs with parameters $\lambda=0$ (triangle-free) and $\mu=2$ (any two non-adjacent vertices have exactly two common neighbors) are known, see the wikipedia page: the 4-...
Florent Foucaud's user avatar
7 votes
1 answer
354 views

Theory of surfaces in $\mathbb{R}^3$ as level sets

Is there a book that treats the classical theory of surfaces in $\mathbb{R}^3$ from the point of view of level sets of a function? I seem to remember someone telling me that such a book exists, but I ...
Otis Chodosh's user avatar
  • 7,077
7 votes
2 answers
347 views

When a localization of a category is (non-)reflective?

Let $S$ be a class of maps of a category $\mathcal{C}$. The localization of $\mathcal{C}$ at $S$ is reflective when the localization functor $\mathcal{C} \to \mathcal{C}[S^{-1}]$ has a fully faithful ...
Valery Isaev's user avatar
  • 4,410
7 votes
2 answers
762 views

Character formula for Lie superalgebras

The Weyl character formula and the denominator identity play important roles in the representation theory of classical simple Lie algebras and Kac-Moody Lie algebras over $\mathbb{C}$ Can you suggest ...
GA316's user avatar
  • 1,219
7 votes
1 answer
280 views

Bicategory of bimodules over internal monoids

In a monoidal category $(C,\otimes)$ one can consider internal monoids and bimodules over these monoids (provided some additional requirements like existence of coequalizers hold). These monoids ...
Marvin Dippell's user avatar
7 votes
3 answers
822 views

Books and resources on PDEs that use Mathematica and Matlab

Can you recommend some reference books that use software like MATLAB and Mathematica to deal with the basic topics in analysis of PDE (the ones you can find in Strauss' book Partial Differential ...
user avatar
7 votes
1 answer
240 views

Are there such things as non-trivial entire semigroups?

I'll state the theorem I am posing up front, and then explain why I think this theorem appears to be true. I am asking if anyone can prove it, or knows references to where it is proved. Please, ...
user avatar
7 votes
1 answer
274 views

Sato-Tate conjecture when Fourier coefficients are complex numbers

Let $k\geq 1$ and let $f=\sum_{n\geq 1}a(n)q^{n}$, $a(n)\in\mathbb{R}$, be a normalised cuspidal Hecke eigenform of weight $2k$ for $\Gamma_{0}(N)$ without complex multiplication. So the result of ...
M.Souf's user avatar
  • 433
7 votes
1 answer
455 views

Analytic properties of Eisenstein series

Let $\Gamma$ be a discrete subgroup of $SL_2(\mathbb{R})$ which has a cusp at $\infty.$ suppose that $\mu(\Gamma\setminus\mathbb{H})<\infty,$ consider the Eisenstein series :$$E(z,s,\Gamma)=\sum_{\...
Med's user avatar
  • 400
7 votes
4 answers
1k views

Minimum negative eigenvalue of zero-one matrices

The following question must have been answered decades ago. For $n$ fixed, what is the most negative eigenvalue among all trace zero zero-one matrices (that is, all entries are either zero or one, ...
David Handelman's user avatar

1
73 74
75
76 77
291