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

**2**

votes

**0**answers

38 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

**3**answers

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

**0**answers

12 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

**1**answer

460 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

**0**answers

31 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

**1**answer

128 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

**2**answers

218 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

**2**answers

92 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

**0**answers

33 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

**2**answers

689 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

**4**answers

807 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

**0**answers

51 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

**0**answers

483 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

**1**answer

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

**1**answer

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

**1**answer

49 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

**1**answer

245 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

**2**answers

767 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

**0**answers

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

**0**answers

142 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

**0**answers

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

**0**answers

214 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

**1**answer

311 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

**0**answers

81 views

### Probability distributions with all positive cumulants

Is there a term for a distribution with all cumulants positive (or nonnegative)?

**1**

vote

**1**answer

127 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

**1**answer

119 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

**0**answers

86 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

**0**answers

121 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

**5**answers

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 ...

**29**

votes

**2**answers

3k 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

**0**answers

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

**0**answers

88 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

**1**answer

163 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, ...

**1**

vote

**0**answers

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

**1**answer

200 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

**0**answers

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

**1**answer

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

**1**answer

142 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

**0**answers

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

**0**answers

217 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 ...

**13**

votes

**2**answers

2k views

### Why are free objects “free”?

What is the origin/motivation for the adjective "free" in the term "free object"?
Does it refer to them coming "for free" (as being constructed from a set in a straight-forward manner) or does it ...

**6**

votes

**2**answers

220 views

### Graded rings with compatible S_n actions

Does the following mathematical gadget have a standard name? Let $R$ be an $\mathbb{N}$-graded ring together with an $S_n$ action on each $R_n$ which are compatible in the following sense. Let $i:...

**17**

votes

**1**answer

707 views

### Tracing the word “form”

Today the word form can refer to (at least) three different kinds of mathematical object:
A homogeneous polynomial. This was apparently started by Gauss (1801), renaming what others had called ...

**56**

votes

**2**answers

3k views

### Does this geometry theorem have a name?

Start with a circle and draw two tangent circles inside. The (black) inner tangent lines to the smaller circles intersect the large circle. The (red) lines through these intersection points are ...

**3**

votes

**0**answers

88 views

### Origin of the terminology “trace operator” related to boundary-value problems for PDEs

Important results in the theory of PDEs regarding boundary-value problems are trace and extension theorems. Since the trace operator essentially acts by restriction to the boundary of the domain, I ...

**-2**

votes

**1**answer

100 views

### Is there a commonly used short name for “squared Euclidean distance”? [closed]

In an optimization program I pass around distance values quite often. In my case these are simple 2D Euclidean distances $\sqrt{\Delta x^2+\Delta y^2}$. Since I want to perform the square root ...

**1**

vote

**0**answers

38 views

### Terminology for initial maps with underlying surjective maps

Let $\omega:\mathcal{C} \to \mathrm{Set}^I$ be a topological functor where $I$ is a set (i.e. a discrete small category). I have to consider maps $f:X\to Y$ of $\mathcal{C}$ such that $X$ is equipped ...

**1**

vote

**0**answers

96 views

### Is there a name for these especially simple directed acyclic graphs, and are any decent characterizations known?

Define the notion of a "foo digraph" recursively as follows.
If we take any finite number of directed path graphs each of which has at least $2$ vertexes, and glue them at the start and end vertexes, ...

**0**

votes

**1**answer

95 views

### What do you call a Markov kernel continuous w.r.t. the weak topology?

Let $X$ and $Y$ be Polish spaces and $K$ a Markov kernel from $X$ to $Y$. That is, $K$ is a mapping $X \times \mathcal{B}_Y \rightarrow [0,1]$ (where $\mathcal{B}_Y$ is the $\sigma$-algebra of Borel ...

**9**

votes

**2**answers

598 views

### Is there a standard name for (non-square) matrices with orthonormal columns?

One encounters often in numerics non-square matrices with orthonormal columns, i.e., $U\in\mathbb{R}^{m\times n}$, with $m > n$, such that $U^TU=I$ (but, clearly, $UU^T \neq I$).
Is there a name ...