Questions tagged [terminology]

Questions of the kind "What's the name for a X that satisfies property Y?"

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Is there a name for relations that are compatible with composition and union?

I’m dealing with relations on relations $\mathcal{R} \subseteq \mathcal{P}(A \times A) \times \mathcal{P}(A \times A)$ that have the following properties: $(R_{1}, S_{1}) \in \mathcal{R} \mathrel\...
Wolfgang Jeltsch's user avatar
2 votes
0 answers
120 views

The notions of "monomial" and "induced monomial" in representation theory

Let $G$ be a group and let $\rho : G \rightarrow V$ over a finite-dimensional vector space. A matrix $M \in \mathbb C^{ k \times k }$ is monomial if every row and every of column of that matrix has ...
RBH63's user avatar
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3 votes
3 answers
699 views

What does "trait" mean?

Looking at some French papers, it seems that the word "trait" is often used to refer to the spectrum of a discrete valuation ring $A$. Does anyone know what the translation of this should be? Is it ...
Kim's user avatar
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5 votes
1 answer
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Can I assign the term "is eigenvector" and "is eigenmatrix" of matrix $P$ in my specific (infinite-size) case?

Remark: I asked this in MSE, the question got views and votes but seemingly no one had an answer so far. Background: I'm rereading a couple of my exploratory (surely not research-level) math-essays ...
Gottfried Helms's user avatar
3 votes
0 answers
92 views

Terminology for set systems: "trace" or "projection"?

Although the following question is not in itself mathematical, it is the expertise/breadth of the research community in mathematics that I wish to appeal to, beyond the filtered/trained search results ...
Yemon Choi's user avatar
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1 vote
0 answers
68 views

The degree of a (combinatorial) selfmap

If $f$ is a map from a finite set to itself, is there any widely accepted definition of the "degree" of $f$? I would like to define deg $f$ as the quantity discussed in Quantifying the ...
James Propp's user avatar
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7 votes
3 answers
328 views

Quantifying the noninvertibility of a function

Given a function $f$ from a finite set $X$ to itself, it seems natural to consider $\kappa_f := (\sum_{x \in X} |f^{-1}(x)|^2)/|X|$ as a measure of the non-invertibility of $f$: it equals 1 if $f$ is ...
James Propp's user avatar
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6 votes
2 answers
810 views

The Floer Equation is Elliptic

Let $(M,\omega)$ be a symplectic manifold and $H \in C^\infty(M \times \mathbb{S}^1)$. Furthermore, let $J$ be an $\omega$-compatible almost complex structure on $M$. The Floer equation is the ...
TheGeekGreek's user avatar
2 votes
0 answers
247 views

Which fields and schemes "have enough finite residue fields"?

I am looking for assumptions on the spectrum $S$ of a field $K$ that ensure the following: there exists an excellent noetherian finite dimensional (integral) scheme $S'$ such that $S$ is its generic ...
Mikhail Bondarko's user avatar
9 votes
2 answers
1k views

Notation for the set of all injections from $A$ into $B$

Is there a common notation for the set of all injections from $A$ into $B$? Some set-theorists use $B^{(A)}$, e.g., A. Levy in his book Basic Set Theory. But some combinatorists use $B^{\underline{A}...
Guozhen Shen's user avatar
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7 votes
2 answers
773 views

Is there a name for this equivalence relation?

Let $M$ be an arbitrary set and let $\mathscr{F}$ be a family of subsets of $M$. Is there a known name for the following equivalence relation or its corresponding partition? $\sim_{M,\mathscr{F}}\,=\...
Guozhen Shen's user avatar
  • 1,288
7 votes
1 answer
783 views

Why is the inertia stack of a smooth Deligne-Mumford stacks called inertia?

Let $\mathcal{X}$ be a smooth Deligne-Mumford stack. Then there is an associated stack $I\mathcal{X}$, called the inertia stack of $\mathcal{X}$. Why is the inertia stack called "inertia"? We can ...
Yuhang Chen's user avatar
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20 votes
2 answers
3k views

Origin of the term "sinc" function

Is the sinc function defined here, really a short form of "sinus cardinalis" as proposed by Wikipedia? This information is deleted now but it existed some time ago. Even if we search Google Books for ...
AChem's user avatar
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5 votes
3 answers
260 views

Is there a name for this "stack" of graphs?

Let $G_1,\ldots,G_m$ be a sequence of graphs, all having the same number $n$ of vertices. For each pair $(G_i, G_{i+1})$ we add $n$ edges that connect the vertices of $G_i$ and $G_{i+1}$ bijectively. ...
Stephan Mertens's user avatar
3 votes
1 answer
575 views

Problem Understanding Euclid Book 10 Proposition 1 [closed]

this is embarrassing, but I am having trouble reading through Proposition 1 of Book 10 of Euclid's elements. I'm struggling with Euclid's terminology and don't have a clear picture of what divisions ...
user304582's user avatar
11 votes
1 answer
785 views

Physicists misuse the term "Kac Moody algebra". Does that bring problems?

In physics textbooks one frequently sees the name (affine) Kac Moody algebra used to describe the universal (one dimensional) central extension of the loop algebra of a semisimple algebra. But this is ...
soap's user avatar
  • 359
0 votes
2 answers
281 views

Naming convention: Adjective for linear operators that are endomorphisms

If a matrix has the same number of rows and columns, we call it a square matrix. The analogous concept for linear operators would be operators with the same domain and range, i.e., endomorphisms. Is ...
Dominique Unruh's user avatar
3 votes
0 answers
376 views

Name for matrices with vanishing row and column sums

Question: is there a special name for matrices whose rows and columns sum to zero? I actually need information about those matrices and thus a keyword for online search. Edit: as there apparently is ...
Manfred Weis's user avatar
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2 votes
1 answer
106 views

Actions that become free after quotienting out their kernel

Let $H$ be the kernel of an action of a group $G$ on a space $X$. Is there a term for the actions with the property that the action of the quotient group $G/H$ on $X$ is free?
R W's user avatar
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6 votes
2 answers
358 views

Symmetric monoidal category with trivial switch morphisms

Is there a specific terminology for a symmetric monoidal category in which for any object $x$ the switch map $x\otimes x\to x\otimes x$ is the identity ? (Or alternatively the action of the symmetric ...
Captain Lama's user avatar
10 votes
1 answer
194 views

Verbal description, or terminology, for the ${\mathcal L}_p$-spaces of Lindenstrauss and Pelczynski

This question is intended for Banach-space specialists and so I will not repeat all the definitions here. My aim is to find out how the Banach space community refers to such spaces in discussions, and ...
Yemon Choi's user avatar
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3 votes
2 answers
472 views

The name of special 16-dimensional hypercomplex number

Let's consider the following number: $n = n_0 + n_1\textbf{i} + n_2\textbf{j} + n_3\textbf{k}$ Where $\{1,\textbf{i},\textbf{j},\textbf{k}\}\subset\mathbb{H}$ and in turn each component can be written ...
Мікалас Кaрыбутоў's user avatar
4 votes
0 answers
641 views

Why are algebraic schemes called algebraic?

In scheme theory, an algebraic scheme is the data of a scheme + a morphism of finite type to the spectrum of a field. Where does the term "algebraic scheme" come from? It does not seem intuitive to me ...
user avatar
3 votes
1 answer
736 views

Which complexes of coherent sheaves are dual to perfect ones?

Let $X$ be a Noetherian scheme that is not Gorenstein but possesses a dualizing complex $D$ of coherent sheaves. Then (if I understand these matters and the answer to the question Characterization of ...
Mikhail Bondarko's user avatar
8 votes
1 answer
551 views

Terminology about G- simplicial complexes

For a simplicial complex $X$ with an action of a discrete group $G$, we can impose the following condition, namely that if $g\in G$ stabilizes a given simplex $\sigma\subseteq X$, then $g:\sigma\to\...
John Pardon's user avatar
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6 votes
0 answers
151 views

What is the name for this type of families?

Is there a common name for a family $\mathscr{F}$ which satisfies the following condition? For any infinite $X\subseteq\mathscr{F}$ there exists a finite $A\subseteq X$ such that $\bigcap A$ is ...
Guozhen Shen's user avatar
  • 1,288
2 votes
1 answer
5k views

Adjacency definition for a directed graph

For an undirected graph, we know that nodes are adjacent to each other if there is a link that connects them. What about adjacency for directed graphs? Is it based on: outgoing links: node $n$ is ...
Ahmed Al-haddad's user avatar
19 votes
4 answers
2k views

Name for abelian category in which every short exact sequence splits

What is the name of the class of abelian categories defined by the following property: every short exact sequence splits?
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1 vote
1 answer
370 views

Simulation of Itô integral processes where integrand depends on terminal (Volterra process)

I need to simulate a process of the form $$X_t=\int_0^t f(s,t)\mathop{dW_s}$$ where $f$ is deterministic and the integral is an Itô integral. I know I can simply take finite Itô sums of discrete ...
Luke Thorburn's user avatar
1 vote
0 answers
152 views

What exactly is and is not a concentration inequality?

Hoeffding's inequality is surely a concentration inequality. It can be written in the form: $\Pr(\bar X + f(n,\delta) \geq \mu) \geq 1-\delta,$ for some function $f$, where $X$ is a set of i.i.d. ...
PThomasCS's user avatar
  • 389
5 votes
1 answer
468 views

Do matrices with only elements along the main and anti-diagonals have a name?

To expand upon the title, I am wondering if there is a specific name for square matrices of the form: $$M = \begin{bmatrix} a_{11} & 0 & \cdots & 0 & \cdots & & 0 & b_{1n} ...
Victoria M's user avatar
3 votes
2 answers
670 views

Is there a name for "splitting a probability distribution into independent components"?

Suppose I have a random variable $\theta=(\theta_1,\dotsc,\theta_n)$; where the $\theta_i$ might have pairwise correlations. I decompose it into $\theta=\hat\theta(\phi_1,\dotsc,\phi_k)$, where $\hat\...
Ted's user avatar
  • 255
5 votes
1 answer
243 views

Smash product and the integers in a Grothendieck $(\infty, 1)$-topos

Let $\mathcal{H}$ be a Grothendieck $(\infty,1)$-topos. According to this page in nlab, for any $X \in \mathcal{H}$, the suspension object $\Sigma X$ is homotopy equivalent to the smash product $B \...
Exit path's user avatar
  • 2,969
46 votes
7 answers
6k views

What is an explicit bijection in combinatorics?

A standard way of demonstrating that two collections of combinatorial objects have the same cardinality is to exhibit a bijection between them. Browsing through some examples (here, there, yonder) ...
Andrej Bauer's user avatar
  • 47.7k
4 votes
0 answers
98 views

Terminology for a foliation that is only tangentially smooth

I'd like to get some information and references, starting with a name, for the following quite common situation, for a smooth (i.e. $C^\infty$) $n$-manifold $M$. A partition $\mathcal{L}$ of $M$ is ...
Pietro Majer's user avatar
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2 votes
0 answers
57 views

Is there a common framework for working with topological base spaces and manifolds?

There is the general construct of a fibre bundle induced by a topological group action. Yet, one of the distinctive differences between this notion and the notion of a vector bundle is that the base ...
Cloudscape's user avatar
3 votes
1 answer
184 views

Cofibrations of functors

Let $\cal M$ and $\cal N$ be model categories, $S,T:\cal M\to N$ functors, and $\alpha:S\to T$ a natural transformation. Say that $\alpha$ is a <blank> cofibration if for any cofibration $i:A\to B$...
Mike Shulman's user avatar
1 vote
0 answers
33 views

Name for a Lower Bound on the Length of General TSPs and ATSPs

Let $G\left(\ V,\ E=V\times V\setminus\lbrace(v_i,v_i)\rbrace,\ \Omega: E\ni e_{ij}\mapsto\omega_{ij}\in\mathbb{R}\right)$ be a(n) (A)TSP instance. Then $$2*\ell(T_{\mathrm{opt}})\quad\ge\quad\sum_{v\...
Manfred Weis's user avatar
  • 12.6k
10 votes
1 answer
485 views

Intuition behind orthogonality in category theory, and origin of name

In category theory, two morphisms $e:A\to B$ and $m:C\to D$ are said to be orthogonal if for any $f:A\to C$ and $g:B\to D$ with $m\circ f=g\circ e$, there exists a unique morphism $d:B\to C$ such that ...
geodude's user avatar
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-3 votes
1 answer
231 views

A common name for a functorial construction of Commutative Algebra?

I am interested whether the following construction naturally appearing in Commutative Algebra has some know and acceped name. Given a commutative monoid $(M,+)$ and a set $X$, consider the family $F(...
Taras Banakh's user avatar
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10 votes
1 answer
325 views

Name for topological spaces where "every point has a local base wellordered by reverse inclusion"?

There are many properties regarding local bases of a topological space, like first countable if every point has a countable local base. Is there a similar name for a space where "every point has a ...
Cla's user avatar
  • 755
0 votes
1 answer
102 views

Name for Directed Edges in Digraphs

Graph theory originated in German speaking countries and there directed edges are called "Pfeil" which translates to "arrow", which makes sense, because arrows have distinguishable ...
Manfred Weis's user avatar
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3 votes
1 answer
3k views

Why is the matrix of all 1's called "J"? [closed]

I've seen J referenced recently in some discussion about algebraic combinatorics, and it took me a while to figure out it was the matrix of all ones. It came up without definition, and I spent too ...
Joe Driscoll's user avatar
9 votes
2 answers
1k views

Terminology about trees

In set theory, a tree is usually defined as a partial order such that the set of elements below any given one is well-ordered. I am interested in the class of partial orders $P$ such that for every $...
Monroe Eskew's user avatar
  • 18.1k
4 votes
0 answers
141 views

Name for facet of a cone containing all but one edge

Let $C \subseteq \mathbb R^n$ be a polyhedral cone, so generated by its edges ($1$-dimensional faces) and $F \subseteq C$ a facet (codimension $1$ face) of it containing every edge except $e$. In ...
Allen Knutson's user avatar
6 votes
2 answers
443 views

Name of a group-like structure

The late Vladimir Arnold, in Arnold, V., Arithmetics of binary quadratic forms, symmetry of their continued fractions and geometry of their de Sitter world, Bull. Braz. Math. Soc. (N.S.) 34, No. 1, ...
Thomas Sauvaget's user avatar
3 votes
0 answers
78 views

Name for mappings that are "not quite projections"

Is there a known name for the following definition? Consider topological spaces $X$, $Y$ and $f: X \rightarrow Y$ a continuous mapping. Then, $f$ is an "almost projection" if there is a topological ...
Vanessa's user avatar
  • 1,368
6 votes
1 answer
288 views

Name of a binary matroid coming from the cycle space of a graph

In some of my recent work, I have 'discovered' a binary matroid which I will describe below. Given a graph $G$, let $H_1(G, \mathbb{Z}/2\mathbb{Z})$ denote the cycle space. This is a vector space ...
Jacob White's user avatar
1 vote
1 answer
341 views

Basis of cone lattice

I only want to know whether a construction that I use appears in literature and maybe has a name already. Let $V$ be a $\mathbb Q$ vector space of dimension $d\in\mathbb N$. A subset $C\subset V$ is ...
user avatar
2 votes
0 answers
115 views

Name for generalization of property: $f^n(x) \ne x$ for all $n > 0$

I am curious about how to specify with standard terminology that a certain function is non-periodic, in the following sense: In the simple case of a unary operation $f: X \to X$, this property would ...
Hans Brende's user avatar

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