Questions tagged [reference-request]
This tag is used if a reference is needed in a paper or textbook on a specific result.
16,063 questions
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Isomorphisms between a double poset and its order-swapped transpose — has this been studied?
A double poset (Malvenuto–Reutenauer, J. Combin. Theory A 118 (2011) 1322–1333) is a finite set $E$ with two partial orders $(E, \le_1, \le_2)$. Foissy (arXiv:1101.5231) uses the involution $\iota(E,\...
- reputation score 11
Score of 8
1 answer
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Reference that integer polynomials have few residues mod $N$ for some $N$
Is there a version of the following result anywhere in the literature?
Proposition 1. Let $p\in\mathbb{Z}[n]$ satisfy $\deg(p)\geq2$, and let $\varepsilon>0$. Then there is $N\in\mathbb{N}$ such ...
- reputation score 14370
Score of 4
1 answer
78 views
Existence of a nontrivial bi-Lipschitz involution of the unit ball fixing the boundary
Let $B(0,1)\subset \mathbb{R}^n$ denote the open unit ball.
I would like to know whether the following statement is true.
There exists a nontrivial bi-Lipschitz homeomorphism
$\phi:\overline{B(0,1)}\...
- reputation score 41
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Average log conductor over squarefree divisors of a squarefree integer at fixed depth is this identity known?
Let $n = q_1 q_2 \cdots q_m$ be a squarefree positive integer with
$m$ distinct prime factors. For $0 \le k \le m$, let $\mathcal{D}_k$
be the set of squarefree divisors of $n$ with exactly $k$ prime ...
- reputation score 1
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Definition of a holomorphic coordinate chart [closed]
A complex manifold is said to admit a holomorphic coordinate chart around a point if there exists a neighborhood $U$ of the point and a map
$$
\varphi : U \to \Bbb{C}^n
$$
such that $\varphi$ is a ...
- reputation score 99
Score of 4
2 answers
367 views
On simultaneous quadratic equations and ternary quadratic forms
Let $$\begin{align}Q_1(x_1)=a_1x_1^2+b_1x_1+c_1\\
= Q_2(x_2)=a_2x_2^2+b_2x_2+c_2\\
= Q_3(x_3)=a_3x_3^2+b_2x_3+c_3
\end{align}$$ be a system of quadratic equations with all coefficients $a_i,b_i,c_i$ ...
- reputation score 141
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Does a single degenerate Clifford algebra carry both $\mathfrak{so}$ (inner derivations) and SDG tangent infinitesimals (its radical)?
In $\mathrm{Cl}(p,q,r)$ (geometric-algebra grading; $r$ = degenerate
directions, $e_0^2=0$) two infinitesimal structures seem to sit side by side in
two different parts of the same algebra.
...
- reputation score 311
Score of 11
1 answer
477 views
Countably many smooth manifolds with boundary
This is likely standard, but I'm having trouble finding a reference that directly states the following. Fix a compact smooth $(d-1)$-manifold $B$, and consider the set of (edited: compact) smooth ...
- reputation score 368
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Modern references on special biserial algebras, strings and bands, and related topics
I am trying to learn about using "strings and bands" to classify indecomposable modules for (special) biserial algebras. I have a scan of a physical copy of Erdmann's "Blocks of Tame ...
- reputation score 321
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Could there be $GF(2^k)$ gadgets for counting using permanent? [closed]
This simple question confused the AIs Gemini, ChatGPT and Claude:
Let $M$ be matrix with integer entries.
Consider the promise that its permanent is $0$ or $1$.
What is the complexity of deciding ...
- reputation score 26055
Score of 9
2 answers
698 views
Book/ lecture notes/articles which elaborate on the history of the development of geometric group theory
I live in a very poor country. I have done masters in mathematics.
I am self studying geometric group theory from the textbook Office Hours with a geometric group theorist and also know text book on ...
- reputation score 1423
Score of 1
0 answers
180 views
Categorification of GW theory
Recently, I was learning about Gromov-Witten (GW) theory in enumerative geometry. I saw there is an interesting conjecture saying that,
All Gromov-Witten cycles corresponding to a smooth projective ...
- reputation score 1853
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120 views
Has Malo's 1895 theorem on Hadamard products been derived as a special case of the Borcea–Brändén real-stability characterization?
Malo's theorem (1895). Consider the polynomials
$$f(x) = a_0 + a_1 x + \cdots + a_m x^m, \qquad g(x) = b_0 + b_1 x + \cdots + b_n x^n,$$
such that the roots of $f$ are all real, and the roots of $g$ ...
- reputation score 11
Score of 3
3 answers
624 views
Practical maximum clique search on 300–900 vertex graphs with only a few seconds available
I am looking for guidance on a practical maximum clique problem.
Suppose I am given an undirected graph $G=(V,E)$, usually with about $300$ to $900$ vertices. I need to find a clique $C \subseteq V$, ...
- reputation score 41
Score of 3
0 answers
84 views
Is there an extension of Mac Lane's "Algebras are $T$-Algebras" for algebraic structures in a monoidal category?
We are trying to prove that certain Hopf algebras equipped with some additional coalgebra morphisms form a category monadic over the category of coalgebras. To this aim, we want to mimik Mac Lane's &...
- reputation score 808