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

9
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0answers
235 views

Why does Loday call the permutohedra “zylchgons”?

Today I was reading Jean-Louis Loday's classic paper, "Realization of the Stasheff polytope", in which he produces a simple and very pretty realization of the associahedra as convex polytopes. He ...
5
votes
1answer
373 views

English translation of “Les aspects probabilistes du contrôle stochastique”

I am looking for an English translation of "Les aspects probabilistes du contrôle stochastique" written by Nicole El Karoui, or knowledge whether it exists. Other references with similar content on ...
0
votes
0answers
53 views

Slow and fast forming singularities of the mean curvature flow

Let $M \times [0, T) \to \mathbb{R}^{n+1}$ be a mean curvature flow and let $T$ be a singular time. Let $A$ denote the second fundamental form. We have a type I singularity if $$ \max_{p \in M} |A(p,...
2
votes
0answers
55 views

How are the unit/counit of a Hopf algebra and of an categorical adjunction related?

For categories $\mathcal{C}$ and $\mathcal{D}$, a pair of functors $\mathcal{C} \xrightarrow{\;L\;} \mathcal{D}$ and $\mathcal{C} \xleftarrow{\;R\;} \mathcal{D}\,$ are an adjoint pair if we have ...
0
votes
0answers
68 views

A (familly) of Lie brackets associated to a Lie algebra

Let $L$ be a Lie algebra whose Lie bracket is denoted by $[.,.]$. For a given vector $V\in L$,does the following 2- linear map always define a new Lie bracket on $L$? $$[X,Y]_V=(adXadY -adYadX)(V)$$...
1
vote
0answers
53 views

Suppressing some but not all terms of a polynomial equation

(I'll ask the question over $\mathbb{R}$, but feel free to change fields if that makes the answer more straightforward or more interesting.) Let $Q$ denote a bivariate quadratic: $$Q(x,y) = Ax^2 + ...
1
vote
1answer
57 views

The Kronecker product of two bipartite graphs' biadjacency matrices: what's it called?

Here's two random $(0,1)$-matrices: $$ A= \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 1 \\ \end{bmatrix} \qquad B= \begin{bmatrix} 1 & 1 \\ 0 & 1 \\ \end{bmatrix}. $$ They can be ...
2
votes
0answers
42 views

What is the ring of functions on the open unit disc with polynomially bounded Maclaurin coefficients called?

Let $R$ be the the set of complex-valued (analytic) functions $f$ on the open unit disc $\mathrm D:=\{z\in\Bbb C:|z|<1\}$ for which there exist constants $a_0$, $a_1$, ... in $\Bbb C$ and $n$ in $\...
7
votes
0answers
279 views

Why are commutative diagrams called “commutative”?

Does anyone know the rationale behind the name of "commutative diagrams"? To be precise, what is(are) the reason(s) for calling those diagrams "commutative" and in what sense? I have previously asked ...
0
votes
1answer
55 views

Standard names of two finitary properties of hypergraphs?

Now we are writing a paper on minimal covers and minimal vertex-covers in hypergraphs and would like to know if there are any standard names for the following two (dual) properties of a hypergraph $(V,...
2
votes
0answers
41 views

Probability Distribution on permutations with factor structure

Say I define a probability measure over the symmetric group $S_n$ as follows: I specify $n$ positive `potential' functions $G_i : \{1, 2, \cdots, N\} \to (0,\infty)$ I then set $$\mathbb{P}(\sigma) =...
25
votes
3answers
4k views

Naming in math: from red herrings to very long names

The are some parts of math in which you encounter easily new structures, obtained by modifying or generalizing existing ones. Recent examples can be tropical geometry, or the theory around the field ...
0
votes
0answers
13 views

Name for Spanning Trees Containing all Edges of a Minimum Weight Perfect Matching

This question is motivated by the task of "uniformly" bicoloring the vertices of a symmetric TSP-instance graph with $2n$ vertices. A simple heuristical requirement for such a bicoloring could be ...
8
votes
1answer
477 views

Whence “Durchschnitt” and “Vereinigung”?

Today the set-theoretic operations of intersection $\cap$ [German: Durchschnitt] and union $\cup$ [German: Vereinigung] are standard. The modern notations are present in the first edition of van der ...
0
votes
0answers
32 views

Name for a variant of the Mellin transform

The Mellin transform is usually expressed as \begin{eqnarray} \mathcal{M}[f](s) &=& \int_0^\infty x^{s-1} f(x)dx \\ \mathcal{M}^{-1}[F](x) &=& \frac{1}{2\pi i}\int_{\alpha -i\infty}^{\...
6
votes
1answer
144 views

Reference request: A collection of topologies on $\mathbb{N}$ formed via series

First, some quick notation: for any series $\sum_{n=1}^\infty a_n$ whose terms are positive real numbers, and for any subset $M = \{m_1, m_2,...\} \subseteq \mathbb{N}$, we write $\sum_M a_n$ to mean ...
2
votes
2answers
226 views

Non-probabilist term for conditional expectation?

When writing an article I encounter what is essentially a conditional expectation - function defined on a bounded interval (not necessarily of unit length) with Lebesgue measure, but information about ...
0
votes
2answers
96 views

Is there a standard name for this type of multidigraph?

A digraph (direct graph) consists of a set $V$ of vertices and a set $E$ of directed edges $v\to v'$. A multidigraph is a digraph in which $E$ is a multiset, so edges may appear multiple times in $E$, ...
1
vote
0answers
34 views

Terminology for 'Sub-Iterated log'

For this question, I write $\log_r n$ to be the $r$-th iterated log: $\log_1 = \log$, $\log_2 = \log\log$, $\log_3 = \log\log\log$, etc; precisely, $\log_{r+1} n = \log(\log_r n)$. Suppose I have a ...
3
votes
2answers
708 views

What is the name of the 65537-gon? [closed]

I know the name of the heptadecagon (17 sides) and the diacosipentacontaheptagon (257 sides). But what is the name of the polygon with 65537 sides? I am unable to figure it.
16
votes
4answers
820 views

Groups that satisfy ${ [x,y]^2 \approx 1 }$

Lately, I have been constructing finite involution monoids that generate varieties with $2^{\aleph_0}$ subvarieties. One construction requires groups that violate the identity ${ [x,y]^2 \approx 1 }$, ...
2
votes
0answers
52 views

Twisted graph duplication

I want to know if the following operation on graphs is already studied or considered somewhere, and if so what it is used for and what it's called. Let $G = (V, E)$ be a directed graph. Define $d(G)$ ...
10
votes
0answers
498 views

A standard name for a function satisfying the intermediate value theorem?

Do you know any (standard) name for a function $f:\mathbb R\to\mathbb R$ having the following weak intermediate value property: $(*)$ for any connected subset $C\subset \mathbb R$ and points $a,b\...
6
votes
1answer
177 views

name for monoids inducing bimonoids in Rel?

Let Rel be the category of sets and relations, which is a (compact closed) symmetric monoidal category under the cartesian product of sets. We write $A \nrightarrow B$ to indicate a relation from $A$ ...
5
votes
1answer
81 views

Name for $\omega_1$-DCC / Noetherian condition?

I recently asked (and then answered) this question: https://math.stackexchange.com/questions/2756777/decreasing-sequence-of-closed-sets-in-a-separable-metric-space. In a separable metric space ...
3
votes
1answer
50 views

Name for Biconnected Tree+Cycle Graph

Is there an established name for graphs, that can be decomposed into a tree with at least three leaf nodes and a connected two-regular graph with the tree's leaf nodes as vertices? examples of ...
9
votes
1answer
246 views

What is the (genuine) name for the Gutik hedgehog?

Working with non-regular topological semigroups, my collegue Oleg Gutik discovered a special space $H$ which we named Gutik's hedgehog. It is homeomorphic to the space $$H:=\{(0,0)\}\cup\{(\tfrac1n,0):...
8
votes
2answers
768 views

How are such sets of natural numbers called?

I heard about this problem an year ago, but I just can't remember the name. The problem goes like this: study the sets $\{a_1,a_2,\dotsc,a_m\}\subseteq\mathbb{N}$ such that if $1\leq i<j\leq m$,...
1
vote
0answers
63 views

Is there a usual technical term for this set-valued function associated to a zero-one matrix?

Let $m$ and $n$ be cardinals, and let $A\in \{0,1\}^{m\times n}$ be any zero-one matrix, considered as a function $A\colon m\times n\to\{0,1\}$. For every $j\in n$, let $A(\cdot,j)^{-1}(1):=\{i\in m\...
3
votes
0answers
148 views

A “surjective implies injective” property for endomorphism rings of modules

Fix a unital commutative ring $R$ and consider a left $R$-module $M$. $\newcommand{\End}{{\rm End}}$ (For the indirect application I have in mind, which would require another post, $\End_R(M)$ will ...
2
votes
0answers
44 views

Is there an established name for bi-module morphisms that swap the module structures?

Let $P,Q$ denote two $R$-bimodules where $R$ is a ring, for my purposes commutative. I'll write the left $R$-module structure by multiplication on the left and analogously for the right structure. ...
8
votes
0answers
219 views

Name for rings with $R \cong R^{\mathrm{op}}$

Is there a name for rings that are isomorphic to their opposite ring $R^{\mathrm{op}}$ in the literature? I'm especially interested for the class of Artin algebras.
6
votes
1answer
316 views

What is this property exhibited by some logical systems?

I'm migrating this question from MSE to MO, as in the span of five months, it received 6 upvotes but no answers. If my language needs to be fine-tuned in any way, constructive suggestions and guidance ...
3
votes
0answers
82 views

Probability distributions with all positive cumulants

Is there a term for a distribution with all cumulants positive (or nonnegative)?
1
vote
1answer
139 views

Name and information about this graph

A certain family of graphs crossed my way while performing some quantum mechanics calculations, and I am very curious whether they have been studied in mathematics before in a different context. Also ...
3
votes
1answer
143 views

“Eccentricity” in the Definition of Graph Center

On the Wikepdia Page Graph Center I saw that the center of graph is the set of vertices with minimal eccentricity, i.e the set of vertices, whose maximal distance to other vertices is minimal. On the ...
2
votes
0answers
87 views

Sphere equation with higher power

The shape described by $x^2 + y^2 +z^2 = 1$ is a sphere. But what do you call the shape described by $x^4 + y^4 +z^4 = 1$? Does it have a name?
3
votes
0answers
125 views

Is the special case of Abhyankar's lemma is also considered as such?

Consider the following statement: Assume $E$ and $F$ are unramified (over some fixed prime) finite separable extensions of a field $K$. Then $EF$ is also unramified. I always thought that it is ...
26
votes
5answers
2k views

Main statement as theorem or corollary

In a text there will often be a few important results that are usually called Theorems. Intermediate statements are called Lemmas, and statements that follow immediately from previous results are ...
30
votes
2answers
4k views

What is quantum algebra?

This might be a very naive question. But what is quantum algebra, really? Wikipedia defines quantum algebra as "one of the top-level mathematics categories used by the arXiv". Surely this cannot be a ...
0
votes
0answers
38 views

Name for Graph Property that is Invariant w.r.t. Change of Vertex Weights

Is there already an established name for properties or subgraphs of finite, symmetric graphs, that are invariant under a change of vertex weights? Some of those invariants are the extremal ...
2
votes
0answers
89 views

What type of boundary (if any) problem for this family of elliptic PDEs? “half boundary”?

Classic literature for a general elliptic PDE with Dirichlet boundary condition is typically studied with the following set up: Let $\Omega \subset R^n$ be some open bounded domain and $\partial \...
4
votes
1answer
172 views

Question about denoting/designating of algebraic structures

I saw this image on Wikipedia (Template:Group-like structures, current revision): Since there are five "properties" that we can have (in this context), namely: totality, associativity, identity, ...
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vote
0answers
95 views

What name can I use for a cocone over the mapping cone diagram?

In homotopy theory, the mapping cone of a continuous map $f\colon X \to Y$ is the homotopy pushout over the following span: $$ \require{AMScd} \begin{CD} X @>{f}>> Y\\ @VVV \\ \{*\} \end{CD} ...
6
votes
1answer
206 views

Singularities at worst like a hyperplane arrangement

Is there a standard name for the type of singularities a codimension-$1$ subvariety of a smooth algebraic variety has when it looks locally (possibly analytically) like an arrangement of hyperplanes? «...
3
votes
0answers
77 views

Poset where every Upper Set has a Greatest Element

Does anyone know of a term for (equivalently) A preorder $P$ where for every $x \in P$ there exists $x_\top \ge x$ such that for any $y \ge x $, $x_\top \ge y $. A preorder $P$ where for every $x \...
2
votes
1answer
247 views

Name for this algebraic structure?

I've found myself looking at a structure $\mathbb{M}$ whose important properties are: $\mathbb{M}$ is a discretely ordered additive monoid. $\mathbb{M}$ has a least element, and this least element is ...
5
votes
1answer
147 views

Classifying functions up to suitable pre-composition and/or post-composition

What's a name for a general technique I've seen used many times? Given any family $\mathcal{F}$ of functions such that $f:X\to Y$ for all $f\in \mathcal{F}$ when one wishes to study in general for an ...
1
vote
0answers
48 views

Opposite of “holistic” for an operator

I am dealing with preference relations, i.e., strict partial orders on a given domain of objects. For example, if $R$ is a preference relation, the preference $a R b$ indicates that $a$ is better than ...
9
votes
0answers
235 views

Is there a reasonable way to define “reductive Lie algebra” in prime characteristic?

Among the finite dimensional Lie algebras over a field of characteristic 0, there is a sensible definition of "reductive Lie algebra" going back at least to the 1960 first chapter of N. Bourbaki's ...