Questions tagged [terminology]

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

Filter by
Sorted by
Tagged with
1
vote
1answer
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
0answers
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
0answers
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
0answers
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
0answers
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
0answers
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
0answers
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
1answer
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
0answers
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
0answers
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
3answers
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
1answer
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
1answer
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
1answer
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
0answers
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
0answers
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
1answer
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
1answer
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
0answers
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
0answers
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
0answers
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
1answer
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
0answers
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
2answers
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
1answer
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
0answers
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
0answers
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
1answer
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
0answers
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
1answer
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
0answers
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
3answers
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
0answers
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
1answer
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
1answer
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
0answers
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
5answers
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
0answers
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
0answers
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
2answers
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
1answer
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
0answers
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
0answers
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
3answers
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
2answers
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
0answers
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
2answers
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
2answers
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
0answers
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
1answer
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 ...

1
2 3 4 5
13