# Questions tagged [terminology]

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

634
questions

**1**

vote

**1**answer

34 views

### Naming convention: looking for better terminology for “centrally symmetric smooth strictly convex bodies”

I have recently found myself researching a certain type of convex body in $\mathbb{R}^2$, namely centrally symmetric smooth strictly convex bodies.
Instead of repeating such a sentence repetitively I ...

**1**

vote

**0**answers

24 views

### Posets which extend centered sets to filters

(Post cross-posted from math.se.)
Suppose $(\mathcal O, \leq)$ is an arbitrary poset. Let us say that $\mathcal O$ is compact if every $\mathcal C\subseteq\mathcal O$ which is centered (any finite ...

**1**

vote

**0**answers

54 views

### What is the standard definition of dual of disconnected planar graph when underlying graph derives 'product structure' over connected graphs?

Dual graph of a plane graph has a standard definition https://en.wikipedia.org/wiki/Dual_graph and an edgeless graph on $n$ vertices is planar. What is the standard dual graph of such a graph?
Update ...

**0**

votes

**0**answers

29 views

### Terminology for exact symplectomorphism

Let $(M,\omega = d\alpha)$ be an exact symplectic manifold. Then a symplectomorphism $\varphi \colon M \to M$ is said to be exact, iff $\varphi^*\alpha - \alpha$ is exact. Is there a terminology for ...

**2**

votes

**0**answers

114 views

### Graphs which are built from complete graphs : Reference request

Let $V$ be a set of $n$ vertices. Fix $3 \le k \le n$. Let $\binom V k$ be the set of all $k$ element subsets of $V$.
We add the edges in $V$ as follows: Let $\mathcal S \subseteq \binom V k$ be ...

**31**

votes

**0**answers

3k views

### The origin(s) of the word “elliptic” [migrated]

The word elliptic appears quite often in mathematics; I will list a few occurrences below. For some of these, it is clear to me how they are related; for instance, elliptic functions (named after ...

**1**

vote

**0**answers

255 views

### Not sure about meaning of a term in English in a French research paper

I am self studying a research paper which is in French and i am not a native french speaker so I used Google Translator and Deepl translator . But I am confused over meaning of a term and have no ...

**5**

votes

**1**answer

101 views

### What is the name of the real form corresponding to the quaternionic symmetric space?

Let $G$ be a compact simple Lie group. Choose a system of positive roots, and let $\mathrm{SU}(2) \subset G$ correspond to the highest root, and $\mathbb{Z}/2 \subset \mathrm{SU}(2)$ the centre. The ...

**2**

votes

**0**answers

112 views

### Why is faithful actions called faithful and who first called it faithful?

Sorry for this question. I asked this on MSE and hsm but no one answered and I decided to post it here that is full of experts.
I want to know why is faithful actions called faithful and who first ...

**1**

vote

**0**answers

83 views

### Is there any name/occurence to this sequence of numbers?

I am curious if there is any name for this sequence of numbers, or any occasion that this sequence is used.
The sequence is $(c_1,c_2,c_3,\cdots)$ with recursive formula
$$c_n=\frac{1}{2n+1}\sum_{i=...

**1**

vote

**3**answers

91 views

### Strictly isotropic and strictly coisotropic submanifolds

Let $M$ be a $2n$-dimensional symplectic manifold. A question: are there special terms for isotropic submanifolds of $M$ of dimensions $<n$ (i.e., isotropic submanifolds that are not Lagrangian) ...

**1**

vote

**1**answer

141 views

### What is a reference for this sort of test set system that avoids all sets of size $\le k$?

My question is: is there a standard name for a structure like the following?
For positive integers $n$, $k < n$ define a "$k$-set-free test for $n$" as a set $C$ of subsets of the integers $\{0, \...

**0**

votes

**1**answer

64 views

### Is there a name for sum of increases of f(x) on ranges where it's growing [closed]

It would be useful for "how hard a biking road is" or "how much could you earn on a particular stock without shorting it".

**1**

vote

**1**answer

157 views

### Terminology: “sufficiently large absolute constant”

I'm currently reading the paper "Random matrices: The distribution of the smallest singular values" by '"Terence Tao and Van Vu" and have run into some terminology which I don't quite (rigorously) ...

**1**

vote

**0**answers

20 views

### Standard terminology for these “coarsening” and “refining” operations for compositions and ordered set partitions?

Let $[M]:=\{1,2,\dots, M\}$. (Part of the twelvefold way) as we all know, there is a bijection between surjective functions $[N] \to [B]$ and ordered set partitions of $[N]$ into $[B]$ blocks (of ...

**2**

votes

**0**answers

44 views

### Is there a name for a tree with all leaf vertices identified with each other?

Is there a name for those graphs that can be formed by taking a tree and identifying all the vertices of degree 1 (leaves) with each other?
Or, if I understand correctly, an equivalent definition may ...

**-1**

votes

**1**answer

54 views

### Is there a common notation to indicate the final form of a simplified definition? [closed]

I'm trying to become better with using proper terminologies and standard notation when taking notes, which lead me to think:
Similar to the indication of a completed proof by use of the Q.E.D. mark, ...

**2**

votes

**1**answer

66 views

### Name for specific cycles in graphs

Is there an established name for cycles $C\subseteq G(V,E)$ with the property that
$$\lbrace u,v\rbrace\subseteq C\cap V\implies\mathrm{dist}_{|C}(u,v)\le \mathrm{dist}_{|G}(u,v)$$
I would be ...

**1**

vote

**0**answers

68 views

### Terminology for transforming a directed acyclic graph into a tree

I am looking for the term of converting a directed acyclic graph (DAG) into a tree by traversing its topologically ordered nodes and copying the subtrees of the nodes with in-degree $> 1$.
Such a ...

**0**

votes

**0**answers

63 views

### Integral transformation, Laplace-like

Is the following integral transformation of $f$ known (for suitable $f$ and $s\in\mathbb{C}$)?
$$
\int_1^\infty f(t) \frac{e^{-ts}}{1-e^{-ts}}dt
$$
It resembles somewhat the Laplace transformation.
...

**0**

votes

**0**answers

69 views

### Path that meets every other path

In a directed graph $G$, what do we call a path, a sequence of edges $$(v_0,v_1),(v_1,v_2),\dots,(v_{n-1},v_n)$$ of length $n$, that intersects every other path of the same length $$(w_0,w_1),(w_1,w_2)...

**1**

vote

**1**answer

128 views

### What do you call a set of vertices that separates the root from the leaves?

Suppose we are given a rooted tree $T$, and a set of vertices $M$ that separates the root of $T$ from its leaves. In other words, every path from the root of $T$ to a leaf contains a vertex in $M$. Is ...

**1**

vote

**0**answers

80 views

### Terminology for representation all of whose isotypic pieces are nontrivial

Let $V$ be a finite-dimensional representation of a finite group $G$. Is there an adjective describing those $V$ for which every irreducible representation of $G$ is a direct summand of $V$?

**7**

votes

**2**answers

367 views

### On a statistic for permutations

Given a permutation $\pi$ we can write $\pi=s_{i_1} ... s_{i_l}$ as a product of simple transpositions $s_i=(i,i+1)$ in a minimal way.
Question 1: Is there an "official" name for the permutation ...

**0**

votes

**1**answer

45 views

### Name for matrix associated to smooth continuation

Is there an established name for the matrices that establish the conditions for a linear combination of $n$ functions $\lbrace f_1(x),\dots,f_n(x)\rbrace$ being the $n$-times smoothly differentiable ...

**4**

votes

**0**answers

117 views

### Is there a name for this slightly stronger version of Cesàro convergence which “more quickly ignores earlier terms”?

Let $V$ be a normed vector space, let $l \in V$, and let $(a_n)$ be a sequence in $V$. We say that $a_n$ is Cesàro-convergent to $l$ if $\frac{1}{n}\sum_{i=1}^n a_i \to l$ as $n\to\infty$.
Now I will ...

**2**

votes

**0**answers

138 views

### Is there a name for a “convex hull with holes”?

If I have a (solid) 3d object, is there a name for the object created from it by taking the convex hull and subtracting from it all points that are on a straight line between any two points on the ...

**4**

votes

**1**answer

116 views

### A name for this kind of lax 2-limit

Consider the following statement of a universal property in a 2-category:
Consider the situation of lax squares:
then what is the name for a universal object $\ell$ equipped with a lax square over ...

**2**

votes

**0**answers

30 views

### Is there a term for a not-necessarily-convex set whose non-extreme points can be expressed as a linear combination of two other points in the set?

This question was asked on Math.SE here, but received no replies after several months. So I have posted it here, though with somewhat revised structuring of the question.
Let $V$ be a real vector ...

**3**

votes

**1**answer

176 views

### Yet another graph characteristic

I wonder if the following graph-theoretical concepts have been considered before, and if so, under which name.
Consider a directed graph $G$ with $n$ nodes.
Let the cycle number $\gamma(\nu)$ be ...

**4**

votes

**0**answers

97 views

### Name for “étale-essential” properties

A map of rings $f:A\to B$ is called "essentially $P$" if there exists some $A\to C\to B$ such that $A\to C$ has property $P$ and $C\to B$ is a localization, that is to say, a filtered colimit of ...

**2**

votes

**3**answers

381 views

### A function in $\mathbb{R}^n$ is equal to its linearization in each point

I have a function $P: \mathbb{R}^n \to \mathbb{R}^n$. This function satisfies:
$$ P(\vec{x}) = J_P(\vec{x}) \cdot \vec{x}$$
where $\vec{x}\in \mathbb{R}^n$, $J_P$ is the Jacobian of $P$ and "$\cdot$" ...

**1**

vote

**0**answers

74 views

### Name for partial orders which are total on connected components

In my context, I encounter a lot of partial orders with the distinguished property that the order is total on connected components. Equivalently, they satisfy the condition
$$x \le y,z \enspace \lor \...

**3**

votes

**1**answer

119 views

### “discrete” objects of a $2$-category

Let $\mathcal{K}$ be a $2$-category. Is there a special name of those objects $B \in \mathcal{K}$ which have the property that the category $\mathrm{Hom}_{\mathcal{K}}(B,C)$ is essentially discrete ...

**0**

votes

**1**answer

58 views

### Ordered $m$-tuples with fixed number of changes

Given $1\leq k\leq m$, $2\leq d\leq c i\ln i$ and $2\leq i\leq c'\ln(mi\ln i)$ at some $c,c'>0$ how many sequences (lower and upper bounds) are of form $$z_1,\dots,z_m$$ on the condition that
$$0\...

**1**

vote

**0**answers

71 views

### Nomenclature: does this coset space have a name?

in my work I tripped on a specific coset space and before starting thinking about it by myself, I wanted to check the literature. However, I do not know if the object has a name (which makes ...

**14**

votes

**5**answers

803 views

### Mathematical words outside of mathematics [closed]

We've all heard expressions like "We need to factor this into the equation," where mathematical words have broader meanings than strictly mathematical. I'd like to develop a collection of such usages. ...

**2**

votes

**0**answers

130 views

### 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\...

**2**

votes

**0**answers

60 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 ...

**3**

votes

**2**answers

348 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 ...

**4**

votes

**1**answer

275 views

### 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-...

**3**

votes

**0**answers

83 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 ...

**1**

vote

**0**answers

62 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 ...

**7**

votes

**3**answers

287 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 ...

**6**

votes

**2**answers

456 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 ...

**2**

votes

**0**answers

228 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 ...

**8**

votes

**2**answers

505 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}...

**7**

votes

**2**answers

754 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}}\,=\...

**0**

votes

**0**answers

14 views

### Discrete time process with linear mixing and multiplicative noise

Consider a stochastic process $\vec{x}^t\in R^N$ in discrete time $t\in N$ which develops according to
$$\vec{x}^{t+1}_i=s_i^t \sum_j A_{ij}\vec{x}^t_j$$
where $A\in R^{N \times N}$ is some matrix ...

**6**

votes

**1**answer

331 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 ...