Questions tagged [terminology]
Questions of the kind "What's the name for a X that satisfies property Y?"
907
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Is there a better name for the "Mayer-Vietoris Octahedral axiom" and has it been studied?
$\newcommand{\K}{\mathcal{K}}$Say $\K$ is a triangulated category with suspension $\Sigma:\K\simeq \K$. In Iversen's book "Cohomology of Sheaves", he doesn't exactly examine triangulated ...
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0
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Can't parse a statement in an article on coalgebras and umbral calculus
This question is cross-posted from MSE.
I am reading Nigel Ray's "Universal Constructions in Umbral Calculus" (1998, published in "Mathematical Essays in Honor of Gian-Carlo Rota", ...
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2
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What is the proper name for this "tersest path" problem in Infinite Craft?
The web game Infinite Craft gives you a starting set of elements $V_0\subset V$ and a mapping $E$ of type $V\times V\rightarrow V$. In fact, $F$ is commutative: $E(v_a,v_b) = E(v_b,v_a)$. So another ...
2
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Is there a name for a normal, projective variety where every effective divisor is ample?
Is there a name for a normal, projective variety such that every effective divisor is ample? Examples of such varieties are projective space, weighted projective spaces, and simple Abelian varieties ...
15
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1
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What is this equivalence relation on topological spaces: there are bijective continuous maps in both directions
Consider the following equivalence relation on topological spaces:
$X\sim Y$ $:\Longleftrightarrow$ there are bijective continuous maps $\phi:X\to Y$ and $\psi:Y\to X$.
Note that there are no ...
2
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1
answer
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Name for generalization of trees to digraphs
One definition of tree in graph theory could be as follows:
A tree is a(n undirected) graph for which there is a unique (undirected) path between any pair of vertices.
This suggest a possible ...
7
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Why is the length spectrum called a spectrum?
Given a hyperbolic surface $X$, one considers the multiset of lengths of closed primitive geodesics. This multiset is called the length spectrum $\mathcal{L}(X)$.
Question: is $\mathcal{L}(X)$ a ...
4
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1
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What are bit strings where all non-trivial rotations match at a minimum number of places called?
Basically, I'm trying to figure out the name of the thing I want to look up. All the terms I've looked up so far have been related, but not close enough to be useful.
I'm trying to find bit strings ...
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0
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Set functions satisfying if $f(X) \le f(Y)$ and $Z \cap (X \cup Y) = \emptyset$, then $f(X \cup Z) \le f(Y \cup Z)$
I am investigating set functions $f : 2^\Omega \to \mathbb{N}$ satisfying the following two properties:
(monotone) For all $X, Y \subset \Omega$, if $X \subseteq Y$, then $f(X) \le f(Y)$.
(property ...
6
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2
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Is there a name for matrices of the form $a_{ij}=\frac{1}{a_{ji}}$?
I have a matrix that is “kind of symmetric.” Specifically, it is an $n \times n$ real matrix such that the entries $a_{ij}=1/a_{ji}$ whenever $j \ne i$. I want to investigate the properties of this ...
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Is the Ordering Principle equivalent to a selection principle?
Working in the context of set theory $\sf ZF$, selection may be defined as a function from nonempty sets to their elements. Formally:
$\operatorname {selective}(c) \iff \operatorname {function}(c) \...
2
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1
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"Potency set" for power set?
Cross-posted at HSM.
Has the term "potency set" been used in English language mathematics for power set, and, if so, what are good references?
It is relevant that for historical reasons, &...
4
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Spaces that are contractible mod diagonal
I bumped into a seemingly natural strengthening of contractibility, which I refer to as "contractible mod diagonal". I'd like to know if this is something standard and whether it appears ...
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0
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if a^x + b^y = c^z, 1/x + 1/y + 1/z < 1, how do we call this numbers?
I have equation
$a^x + b^y = c^z, 1/x + 1/y + 1/z < 1$, where $a$, $b$, $c$, $x$, $y$, $z$ are positive integers.
Are there any special name for solutions of this equation?
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Name for a product of actions / dynamical systems
Suppose $G \curvearrowright X, H \curvearrowright Y$ are group (or monoid) actions, or dynamical systems. Then $X \times Y$ is a $G \times H$-system of the same type in the obvious way by $(g, h) \...
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What should we call the area for which the lower border is a Motzkin path?
We can draw a Motzkin path from $(0,0)$ to $(n/2,n/2)$ using steps $(0,1)$, $(1,0)$ and $(1/2,1/2)$, such that the path never goes below the line $y=x$. Consider the area bounded by the Motzkin path, ...
2
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0
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Root system terminology
Let $\Phi$ be a root system. In a paper I'm writing, I need to work with subsets $\Phi' \subset \Phi$ satisfying the following two conditions:
For all $\lambda_1,\lambda_2 \in \Phi'$ and $c_1,c_2 \...
0
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1
answer
558
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What is this three dimensional curve that looks like an infinity sign called?
What is this three dimensional curve that looks like an infinity sign called? (Is there a known parametric equation for it?)
It was generated with this Sagemath - script, where you can zoom in 3d in ...
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0
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Is there a standard name for the following class of functions on non-Hausdorff manifolds?
Let $M$ be a (not necessarily Hausdorff) smooth manifold. Given an open chart $U\subset M$ and a compactly-supported smooth function $f:U\to\mathbb{R}$ on $U$, define $\widetilde{f}:M\to\mathbb{R}$ by ...
2
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0
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Name for isomorphisms canonically identifying all elements in a category
Say in a category, for any two objects $A,B$, we have an isomorphism $\iota_{AB}:A\to B$ with the property that $\iota_{BC}\circ\iota_{AB}=\iota_{AC}$ and $\iota_{AA}=\mathit{id}$.
Essentially, such a ...
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How did the term "space" in mathematics started to be understood as a set with a structure?
In mathematical literature, the term 'space' is often used to describe a set endowed with additional structure, such as a metric space or a vector space. What is the historical evolution of the ...
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A face and all its neighbors: terminology?
Suppose $F$ is a face of a 2-complex, and $F_1,\dotsc,F_n$ are the faces that are adjacent to (i.e., share an edge with) $F$. Is there a standard term for a collection of faces of the form $\{F,F_1,\...
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0
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Why N-1 and N-2 rings are called like that?
In the Stacks Project, Tag 032F, we find:
Definition. Let $R$ be a domain with field of fractions $K$.
We say $R$ is N-1 if the integral closure of $R$ in $K$
is a finite $R$-module.
We say $R$ is N-...
3
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0
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Names for split Lie groups
Do any of the simply connected simple Lie groups of the split real classical Lie algebras have names other than “the universal cover of _”?
0
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0
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Does there exist an established name for the exponential of surprisal (e.g. the reciprocal of probability?)
There are several different names that I know of for the exponential of the entropy of which "diversity" and "perplexity" are fairly well-established. Tom Leinster has a very ...
5
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2
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Is there a name for this family of matrices?
Let $0<a_1<a_2<\cdots<a_n$ and let $A$ be the symmetric $n\times n$ matrix with
${ij}^\text{th}$ entry $A_{ij}=\min\{a_i,a_j\}$.
For example, if $a_i=i$ for each $i\le n=5$ then
$$A=\begin{...
3
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0
answers
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A higher-dimensional "line of curvature"?
Let $M$ be a submanifold of a Riemannian manifold $Q$, and let $\Gamma$ be a $d$-dimensional submanifold of $M$, i.e., $\Gamma^{d} \subset M \subset Q$.
Suppose that, for all (unit) normal vectors of $...
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Who introduced the term hyperparameter?
I am trying to find the earliest use of the term hyperparameter. Currently, it is used in machine learning but it must have had earlier uses in statistics or optimization theory. Even the multivolume ...
2
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0
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287
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Does this monoid have a name?
Fix a positive integer $n \geq 1$. Let $M$ be the monoid with generators $S=\{x_0,x_1,\ldots,x_n\}$ and relations $R = \{ \alpha x_0 = \beta x_0\colon \alpha,\beta \in S^*, |\alpha|=|\beta|\}$, where $...
5
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1
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Topological property of convergent sequences being eventually constant
Is there a name in the literature for the topological property that all convergent sequences are eventually constant?
This property seems to occur with some frequency and it would be nice to have a ...
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0
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Edge contractions of a graph but only along maximum cliques
Consider the following operation to an undirected graph: one is allowed to take any maximum clique and replace the clique with a single vertex which is attached to every single vertex which has an ...
2
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1
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Name for a sum of dyadic vector products
Question:
is there a name for the following operation
$$\sum_{i=1}^n\sum_{j=1}^mx_iy_j^T,\ x_i,y_j\in \mathbb{R}^k$$ i.e. for generating a square matrix that is the sum of the cartesian product of a ...
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Referring to the countability of $\Bbb Q$ as "Cantor's first diagonal argument"
I had a discussion with one of my students, who was convinced that they could prove something was countable using Cantor's diagonal argument. They were referring to (what I know as) Cantor's pairing ...
4
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0
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What does it mean "parallel"?
I am thinking on a strict definition of the notion of parallel affine sets in a linear space and came to the following
Definition 1: An affine set $A$ is parallel to an affine set $B$ in a linear ...
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1
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What is the history of the term "faithful functor"?
Is it known who coined this term and what he meant? By comparison, the association between "full" and "surjective on $\mathrm{Hom}$" doesn't sound so cryptic. (I understand, of ...
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Functors, forming pairs "coretraction–retraction", what are they called?
I asked this two months ago at MathStackExchange, but without success, so I hope that somebody at MO could help.
Let $I$ and $K$ be two categories. Let us consider two functors from $I$ to $K$:
a ...
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Group homomorphism from $\mathrm{GL}_p$ to $\mathrm{SL}_p$ in characteristic $p$
If $k$ is a commutative field of characteristic $p>0$, then the map
$$ \theta \colon \mathrm{GL}_p(k) \to \mathrm{SL}_p(k) \colon A = (a_{ij}) \mapsto (\det A)^{-1} (a_{ij}^p) $$
is a group ...
2
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1
answer
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What is the name of a 8-regular graph on $\mathbb Z^2$?
There are many (planar) lattices: standard square grid lattice, hexagonal lattice, triangular lattice, Lieb lattice, Kagome lattice, dice lattice...
Consider the standard square lattice on $\mathbb Z^...
2
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0
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Name of this geometric point? [closed]
Draw a triangle. At one of the vertices, draw a line through it that bisects the angle. At each of the other two vertices, draw a line through it which is perpendicular to the line that bisects its ...
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1
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Reflective functors?
Let $C_0\subseteq C$ and $D_0\subseteq D$ be reflective subcategories with reflection functors $r_A$ and $r_B$. For any functor $F:C\to D$, we may consider the natural transformation $r_BF\eta_A:r_BF\...
2
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0
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The canonical automorphism of the symmetric group
Let $S_n$ be the symmetric group of order $n$. Denoting simple transpositions by $\sigma_i$ the collection $\sigma_1, \dots, \sigma_{n-1}$ generates $S_n$ subject to the following relations:
$$
\sigma ...
1
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0
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A one-sided/monotone version of min/max-stable distributions -- does this have a name?
In a couple of papers I am working on (in random graph theory) I have encountered the following property of certain probability distributions, which I will describe shortly, and I am wondering if this ...
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0
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Is there a name for this condition on a monoid?
Suppose we have a commutative monoid ${\mathcal M}=\langle M,\otimes\rangle$ such that the usual divisibility relation $\leq_\otimes$ given by $a\leq_\otimes b\Leftrightarrow \exists c(a\otimes c=b)$ ...
1
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1
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does this relation associated with a poset have a name?
Given a partial order $P$ on a set $S$ does the set of ordered pairs $(x,y)$ in $S\times S\setminus P$ such that $P\cup\{(x,y)\}$ is a partial order have a name? (If so then it would apply to all ...
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Name for a specific kind of regular hyper graphs
Question:
is there already an established name for the following kind of hypergaphs:
given a set $\mathfrak{V}$ with $n\lt\infty$ elements
the hyper vertices $\mathfrak{v}\subseteq \mathfrak{V}$ are ...
3
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1
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Terminology for a subtree of a rooted tree with a path boundedness property
I'm not a graph theorist, so I apologize if some of the following terminology isn't quite correct.
Let $(T,f,v_0)$ be a complete degree $d$ rooted tree (definition at the end).
Definition. Let $m\ge0$....
0
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0
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A name for "anti-symmetric" Frobenius algebras?
Let $V$ be an $N$-dim vector space and denote its exterior algebra by $\Lambda^{\ast}(V)$. The algebra $\Lambda$ has an obvious Frobenius algebra structure $B(-,-)$ given by wedgeing and then ...
5
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2
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Terminology for ordinals whose constructible level is the least one satisfying some formula
An ordinal $\alpha$ is "meta-definable" by some formula $\varphi$ without free variables if:
$$
\begin{cases}
L_\alpha \models\varphi \\
\forall\beta < \alpha \, L_\beta \not\models \...
0
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0
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71
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Merging two composable walks in a graph
Let $G$ be a graph (i.e., an undirected graph in which we allow for loops and parallel edges). Denote by $V$ the vertex set, by $E$ the edge set, and by $\psi$ the incidence function of $G$, and let $\...
3
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1
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name for products of the form $\prod_i (1 + a_i t^i)$
In the context of generating functions, is there an established name for (infinite) products of the form $\prod_i (1+a_it^i)$, or perhaps more generally $\prod_i (1+f_i(t))$, assuming that the ...