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 order-preserving functions $f$ where “$a\le b$ if and only if $f(a) \le f(b)$”? [closed]
This is something only slightly stronger than monotonicity. I think that in category theory this would be a fully faithful functor, but I’m not sure if there is a standard name for this in order ...
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Terminology: Existence + Representation
I'm looking to describe a result in a recent paper of mine, but I don't know if there is a term used for a result which is both an existence theorem and a representation theorem.
Specifically, the ...
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Why the name `Lipschitz-Free Banach spaces'?
There are many names for the same objects that is known as the Arens--Eells spaces, transportation cost spaces, free Banach spaces over a (pointed) metric space, and Lipschitz-free Banach spaces.
The ...
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Reference request for linear matrix inequality with PSD matrices
In literature, people say a spectrahedron is the following set
$$\left\{x \in \mathbb{R}^d : x_1 A_1 + \cdots + x_d A_d \geq B \right\}$$
where $\geq$ is in the positive semidefinite sense. Is there a ...
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Is there a name for and/or reasonably nice characterisation of "mixingly physical" measures?
Let $M$ be a Riemannian manifold with volume measure $\lambda$, let $f \colon M \to M$ be a diffeomorphism, and let $\mu$ be a probability measure on $M$ with compact support.
As stated in the ...
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What is a bipartite hypergraph?
Bipartite graphs are very useful, and I am looking for a generalization of this concept to hypergraphs. I found two different definitions of bipartite hypergraphs:
In the Wikipedia page Hypergraph, a ...
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Why aren't $B_n$ and $C_n$ the other way around?
In the classification of complex simple Lie algebras/groups, I have always been vaguely puzzled why $B_n$ and $C_n$ are labeled the way they are. I always instinctively want to put the special ...
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Emergence of the orthogonal group
Do we know what mathematician first considered, and perhaps named, what we call the group $\mathrm O(n)$, or $\mathrm{SO}(n)$, for some $n>3$?
I mean it specifically as group (not Lie algebra) ...
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Is there a name for $f(M, x) = x^\top M x$? [closed]
I often encounter things of the form $x^\top M x$, where $M$ is symmetric positive (semi-)definite. Is there a term for that? I know related terms:
We can say $M$ is a bilinear form, $M(x,y) = x^\top ...
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The name for an assumption made for the sake of contradiction
What is the name (or adjective) for an assumption made for the sake of contradiction?
To be clear, I'm in search of an expression in the form "a(n) $\underline{\quad \quad \quad \quad}$ ...
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Is there a proper name for those 'shifted moments'?
Suppose that we have a random variable $X$, $i \in \mathbb N$, and a scalar $t$. Is there a proper name for these integrals, that I for the moment call 'shifted moments' ?
$$I_{i}^{t} = \mathbb{E}\...
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Is there a name for commutative algebras over a field $k$ whose residue class fields have finite dimension over $k$?
Let $k$ be a field and let $A$ be a (commutative) $k$-algebra. Assume that for every maximal ideal $P \subseteq A$ the residue class field $A/P$ has finite dimension as a $k$-vector space.
Is ...
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Why are quotient sets (types) called quotients -- are they the inverse of some product? [closed]
There seems to be a beautiful relation between natural numbers and sets (and types),
as in the size of a discriminate union, cartesian product, and function type,
is described by the sum, product, ...
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Terminology introduced in recent years with more than one meaning
Suppose a term(inology) is recently (in last 20 years) introduced in research mathematics.
It might happen that some one who wish to use it, in the same area of research, for different purposes or ...
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"Anti-Leibniz order"
It seems that some people use the term "anti-Leibniz order" for what I'd call the "diagrammatic order" of composition: writing $f;g$ for the composition of $f$ and $g$ instead of $g\circ f$.
(I have ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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The origin(s) of the word "elliptic"
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 ...
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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 ...
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Why are faithful actions called faithful and who first called them 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 are faithful actions called faithful and who first ...
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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=...
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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) ...
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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, \...
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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".
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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) ...
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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 ...
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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 ...
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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, ...
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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 ...
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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 ...
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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.
...
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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)...
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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 ...
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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$?
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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What do you call an object constructed as part of a proof?
I find myself wanting to talk about parts of a proof, e.g. the role played by mathematical expressions within a proof.
When proving a theorem it is common to construct some kind of object and then ...
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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}$$
where $\vec{x}\in \mathbb{R}^n$, $J_P$ is the Jacobian of $P$ and "$\cdot$" ...
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Name for partial orders which are total on connected components
In my context, I encounter a lot of partial orders with the distinguished property that the order is total on connected components. Equivalently, they satisfy the condition
$$x \le y,z \enspace \lor \...
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"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 ...
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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\...
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