Questions tagged [reference-request]
This tag is used if a reference is needed in a paper or textbook on a specific result.
14,543
questions
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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
$$
\...
7
votes
1
answer
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What are current trends/questions in algebraic logic?
What are current trends/questions in algebraic logic? I mean the research developed by Paul Halmos.
Could anyone give some references for the overview of its history? Any overview of its application ...
7
votes
2
answers
509
views
Recovering a Weighted Graph from Shortest Path Distances
I am interested in the following problem (A) and its related formulation (B).
(A) Suppose that $G = (V,E,w)$ is an unknown weighted graph on the vertex set $V$ and that one has access to $d_G(v,v'), \...
7
votes
1
answer
639
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The Irreducible Corepresentations of the eight-dimensional Kac-Paljutkin Quantum Group
I asked this question on Math.Stack but have not had any answers.
Question
What are the irreducible corepresentations of the eight-dimensional Kac-Paljutkin Quantum Group, $A$?
The trivial ...
7
votes
2
answers
996
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For what spaces is the Hardy-Littlewood maximal operator of strong type $(p,p)$ if and only if $p > p_0 > 1$?
(This is essentially a continuation of my previous question, here.)
Let $(X,d,\mu)$ be a metric measure space, i.e. $\mu$ is a Borel measure on the metric space $(X,d)$. Further assume (though you ...
7
votes
2
answers
1k
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Internal Day convolution
Let me recall that any small category $\mathbb{A}$ enriched in a complete and cocomplete symmetric monoidal closed category $\mathbb{V}$ admits embedding (the Yoneda embedding):
$$y_\mathbb{A} \colon \...
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 ...
7
votes
1
answer
381
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Status of the Isomorphism problem for automatic groups?
I only ask because I don't know how to look for the answer.
7
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2
answers
577
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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 ...
7
votes
1
answer
480
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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.
...
7
votes
1
answer
2k
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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
$$\newcommand{\ff}{{}_1F_1}
\ff(b+k;b;z)\...
7
votes
1
answer
533
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GCH+ Kurepa Families
I have a couple of questions about known theorems for GCH+Kurepa families.
Definition first: Let $\kappa$ be a infinite cardinal. A $\kappa^+$ Kurepa family is a family $F$ of subsets of $\kappa^+$ ...
7
votes
1
answer
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The Correlation of the Möbius Function and Dirichlet Characters
Let $\chi$ be a Dirichlet character, and define $\phi_\chi (n)$ so that it satisfies $$\sum_{n=1}^\infty \phi_\chi (n)n^{-s}=\frac{\zeta(s-1)}{L(s,\chi)}.$$
In other words
$$\phi_{\chi}(n)=\sum_{d|...
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 ...
7
votes
1
answer
919
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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 ...
7
votes
1
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949
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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 ...
7
votes
1
answer
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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 ...
7
votes
1
answer
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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 ...
7
votes
3
answers
884
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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 ...
7
votes
1
answer
312
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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 ...
7
votes
1
answer
200
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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 ...
7
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1
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281
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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 ...
7
votes
2
answers
822
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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 ...
7
votes
1
answer
201
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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 ...
7
votes
2
answers
236
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Congruences of binomial sums
Let $a_n$ is a binomial sum, for example
$$
a_n := \sum_{k} \binom{n-k}{k} \quad \text{or} \quad \sum_{k=0}^n\binom{n+k}{n-k}\binom{2k}{k}
\quad \text{or} \quad \sum_{k=0}^n\sum_{\ell=0}^k\binom{n}{k}\...
7
votes
1
answer
387
views
Combinatorial reciprocity for symmetric functions
I am wondering whether a certain instance of combinatorial reciprocity (in the sense of Stanley's classic paper "Combinatorial Reciprocity Theorems"), concerning symmetric functions, is ...
7
votes
2
answers
468
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Finite generation of motivic cohomology of number fields
Let $F$ be a number field ($F=\mathbb Q$ is fine for my purposes) and let $n\geq2$ be an integer. Is it known whether the first motivic cohomology groups
$$\mathrm H^1(\mathrm{Spec}(F),\mathbb Z(n))$$
...
7
votes
1
answer
460
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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 ...
7
votes
1
answer
326
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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 ...
7
votes
1
answer
213
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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 $...
7
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3
answers
320
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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 ...
7
votes
1
answer
257
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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 ...
7
votes
1
answer
469
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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 ...
7
votes
1
answer
657
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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 ...
7
votes
1
answer
817
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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{...
7
votes
1
answer
255
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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):
$$...
7
votes
2
answers
239
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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 ...
7
votes
1
answer
440
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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 ...
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-...
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 ...
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-...
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 ...
7
votes
2
answers
347
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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 ...
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 ...
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 ...
7
votes
3
answers
822
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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 ...
7
votes
1
answer
240
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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, ...
7
votes
1
answer
274
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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 ...
7
votes
1
answer
455
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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_{\...
7
votes
4
answers
1k
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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, ...