0
votes
0answers
45 views

Has this partition a name?

The decomposition in disjoint cycles in $S_n$ was inspiring for this question. I found out (if I did nothing wrong) that more generally a bijection $f:X\rightarrow X$ induces a partition of $X$ ...
1
vote
0answers
35 views

Building a function $p : \mathcal{D} \rightarrow \mathbf{Ord}$ from a faithful functor $U : \mathcal{C} \rightarrow \mathcal{D}.$

For simplicity, I will ignore size issues in this question. Let $\mathcal{D}$ and $\mathcal{O}$ denote categories. By a function $\mathcal{D} \rightarrow \mathcal{O},$ let us mean a functor from the ...
1
vote
0answers
29 views

In regards to metric spaces, does $d^\star$ have an accepted name, or notation? Do any authors use it?

(I write $\omega$ for the set $\{0,1,2,\ldots\}$.) Let $X$ denote a metric space with metric $d$. Define a function $d^{\star} : X^\omega \times X^\omega \rightarrow [0,\infty]^\omega$ by writing ...
2
votes
0answers
25 views

Have any authors suggested mathematics-wide prefixes for “missing a quotient” and/or “missing an identity”?

The prefixes in the following terms both mean: "missing the obvious quotient by the obvious equivalence relation." seminorm pseudometric Similarly, the prefixes in the following terms both mean: ...
1
vote
0answers
46 views

Why is it called a primitive root?

I am looking for a paper or reference that explains why primitive roots are called primitive roots. I know what they are but was wondering if there was a reason?
5
votes
0answers
32 views

Name for Number of Ancestors/Descendants of Vertex in Directed Acyclic Graph

Let $G = (V, E)$ be a directed acyclic graph. For each vertex $v \in V$, define the ancestors of $v$ to be the set of vertices $u \in V$ such that there exists a directed path from $u$ to $v$. ...
1
vote
1answer
47 views

When is a binary operation bipotent?

I learnt that $\max(-,-)$ is a bipotent binary operation but I'm not able to find a definition of bipotent operation. QUESTION A binary operation $*:M\times M \rightarrow M$ is bipotent if ...
0
votes
0answers
24 views

Terminology in universal algbera

(Fix throughout a functional language $\Sigma$.) Given an algebra $A$ with underlying set $\vert A\vert$, there is an obvious surjective homomorphism from $A$ to the free algebra generated by $\vert ...
3
votes
1answer
49 views

Sets that are equal to closure of its interior

Is there a standard name for set $M$ for which $M = \overline{M^0}$? $M^0$ is interior and $\overline{M}$ is closure. Often I work with well behaved sets and functions. I have in mind continuous ...
2
votes
0answers
110 views

How mathematical theorems and concepts gain their names?

Cantor's theorem, Woodin Cardinal, Sacks Forcing and Martin's Axiom are just some of well-known theorems and concepts of mathematics which have the name of those mathematicians who introduced these ...
1
vote
0answers
21 views

Standard deviation and related quantities

By definition, standard deviation is the square root of the variance. There is some common terminology for the quantities $$\mathbb{E}(|X-\mathbb{E}X|^p)^{1/p} $$ for $p \geq 1$? Or, they are just ...
3
votes
0answers
23 views

Is there a name for this partial order between metrics?

Suppose we have a set $X$ and two metrics $d_1,d_2$ on it (which may or may not attain $\infty$). Assume furthermore that $d_1,d_2$ have the same metric components (where a metric comoponent is a ...
0
votes
0answers
44 views

Ring $R$ as $R[x]$-module

My professor mentioned some interesting examples of modules, giving as an example the following two: $R$ as an $R[x]$-module, in which multiplication by $x$ was taken to be evaluation under a fixed ...
3
votes
1answer
79 views

What are some examples of “homogeneous” linear orders, other than $\mathbb{R}$ and $\mathbb{Q}$?

Let $L$ denote a linear order that is unbounded. Then it may or may not satisfy: Globally homogeneous. For all $x,y \in L \cup \{-\infty,\infty\}$, if $x < y$ then the interval $(x,y)$ is ...
0
votes
0answers
28 views

An interleaved path of arrows in a category/digraph

In what I am doing now, a slightly strange concept emerged; My objects are sequences of arrows $\{f_i\}_{i=1}^{n}$ in a small category such that for every $1\leq i\leq n-1$, there is an arrow from the ...
0
votes
0answers
142 views

Collections of Homomorphic (defined) structures via $f$

Long ago I read a text about a collection of algebraic sturctures all homomorphic (or isomorphic) via a unique homomorphism An Example similar to the construction I found was this: Lets take define ...
3
votes
1answer
57 views

Name/significance of integral of the square of a probability density function

Background/Motivation Given a probability density function $f(x)$, the mean of the corresponding random variable is the $x$-coordinate of the centroid of the region under the graph of $f$. I ...
5
votes
0answers
46 views

Is there a name for the algebra of substructures?

Let $X$ denote an entropic algebra (see here), which just means that all the operations of $X$ are homomorphisms $X^n \rightarrow X.$ Abelian groups are the classic example. Then for any operation of ...
4
votes
2answers
102 views

Have action/predicate systems (or similar) been considered in the literature?

Question. Has the following concept, or anything similar, been considered in the literature? Definition. An action/predicate system consists of sets $A$ (the actions) and $X$ (the predicates) such ...
4
votes
1answer
83 views

Weakened associativity axiom: $(x * y) * z \leq x*(y*z).$

Call a partially ordered magma $(X,*)$ sub-associative iff it satisfies the following axiom. $$(x*y)*z \leq x*(y*z).$$ Basically, this is saying that we may shuffle brackets right to get a larger ...
1
vote
0answers
24 views

What is the name of this type of stochastic processes?

I've seen someone briefly define a continuous time stochastic process $X$ on $\mathbb{N}$ as the (a?) solution to $$X(t)=X(0)+Y\left(\int_0^t f(X(s))ds\right)$$ where $Y$ is an inhomogeneous ...
2
votes
0answers
70 views

Do subhomomorphisms / subfunctors have a standard name, and where can I learn more?

Sorry for all the mistakes in the original! I think they're mostly fixed now. Thank you for your patience. Part 1. If $A$ and $B$ are models in $\mathrm{Pos}$ of an algebraic signature $\sigma$, ...
0
votes
1answer
46 views

Adding together curves or shapes to approximate something more complex

I'm looking for proper terminology / references for the following sort of problem: Say we have some one-dimensional curve like $y = 10$ defined over the real valued domain $[0,1]$, and we ask, how ...
2
votes
0answers
50 views

Taking the (pseudo)inverse of a monoid operation.

Let $M$ be a monoid with binary operation $f : M \times M \to M$. I'm interested in functions $g : M \to M\times M$ that obey the property: $$ f(g(m)) = m $$ I want to understand what all of the ...
1
vote
1answer
43 views

What do you call a convex polyhedron whose symmetry group is transitive on the facets?

I'd like to know a name/source for the following concept: Let $P$ be a convex polyhedron in $\mathbb{R}^3$. Let $G$ be its symmetry group, and let $F$ be the collection of (top-dimensional) faces of ...
1
vote
1answer
42 views

What is the name of this factor-algebra?

In the polynomial algebra $k[x_1,x_2,\ldots, x_n]$ consider an ideal $I$ generated by the polynomials of the form $x_i^k-x_i$, $i=1 \ldots n$ and $k=2,3,\ldots.$ Consider the quotient algebra ...
1
vote
2answers
84 views

What is this mathematics sub-field called?

I would love to answer another question on this site, but I am totally unfamiliar with the required technique. I mean, I don't even know the sub-field's name. The field I am looking for is one that ...
1
vote
2answers
106 views

Partial functions - where can I learn more about this (heuristic, informal) system of conventions?

Is there a name for the following (heuristic, informal) system of conventions for dealing with partial functions and undefined expressions? I'd like to know whether it has any undesirable quirks that ...
3
votes
1answer
82 views

Completing a Partially Defined Associative Binary Operation

This is more like a question about terminology. I would like to hear some recommendations of books that discuss algebraic structures with one partially defined associative binary operation, and the ...
1
vote
0answers
36 views

Is there a special name for matrices with $M[j,i] = M[i,i] - k, i \neq j$?

Backgroud: I am working on a computer science problem and arrives at a matrix $M$ with the following property: The size of Matrix $M$ is $n\times n$. For each row $j$, we have $M[j,i] = ...
6
votes
1answer
85 views

name of the unit of adjunction between $-\times C$ and $\cdot^C$

Answers to a earlier question about the categorical interpretation of first-order quantification led me to learn more about adjoints. Now, I understand that a category $\mathscr{C}$ with products has ...
0
votes
0answers
86 views

Morphisms in Bourbaki “Theory of Sets”

In Bourbaki "Theory of Sets" there is notion of "morphisms" and different kind of morphisms such as "initial morphisms". These are defined in terms of order theory. It seems that Bourbaki treatment ...
2
votes
1answer
51 views

characterization of certain idealizers of submodules

Consider two commutative rings with identity, $R$ and $S$ where $R$ is a principal ideal domain, $S$ is free and finitely-generated as an $R$-module and suppose there is a $R$-module homomorphism ...
5
votes
1answer
133 views

Languages with context-free grammar having only one non-terminal symbol

As seen in this question, the class of languages that can be generated by a context-free grammar having only one non-terminal symbol (i.e. the start symbol) is a proper subclass of the class of ...
0
votes
2answers
96 views

Changing the index of a summation - what is it called?

About $\sum$ (summation), what is it called when you change the index of a summation? My teacher does it all the time and I just don't get it! Please send some links so I can learn it.
6
votes
4answers
390 views

Different meanings of math terms in different countries

Does anyone know of a list of math terms that have (slightly) different meanings in different countries? For example, "positive" could mean $\geq 0 $ in some places, and "strictly positive" means ...
4
votes
3answers
106 views

What does boson-type realization mean?

I have seen several different contexts the expression "boson-type realization", for instance in the study of algebras growth and realization of affine algebras. To be or not be a boson-type ...
4
votes
1answer
65 views

Is there a standard name for this semigroup?

Given a semigroup $X,$ we can form a new semigroup $Y$ by asserting that: the carrier of $Y$ is the set $X^2$, and the law of composition in $Y$ is given by $(a,b)(a',b')=(aa',b'b).$ Finally, ...
5
votes
1answer
102 views

Is the variant direct image mathematically significant?

Preimages have the property that for an arbitrary function $f : X \rightarrow Y$ and all $B \subseteq Y$ it holds that $$f^{-1}(B^c)=[f^{-1}(B)]^c.$$ However, the analogous statement for direct ...
3
votes
1answer
73 views

The 'compactness cardinal' of a space

I'm looking for references (and a name!) for the following invariant of a topological space $X$: The least (infinite) cardinal $\kappa$ such that any open cover of $X$ has a subcover of cardinality ...
8
votes
1answer
355 views

Is “cofunctor” an accepted term for contravariant functors?

People are used to the prefix co- flipping arrows in a concept1, and I have seen people using cofunctor to mean a functor that flips arrows, i.e. that takes $A \to B$ to $FB \to FA$. I know this ...
2
votes
0answers
42 views

Usage and determination of “rank” and “dimension” of groups & representations

Physicist here. I seem to see conflicting statements about the rank of some groups I've come across lately. A paper I'm reading states that $SO(6)$ is rank 3 and therefore its Cartan subalgebra ...
12
votes
1answer
383 views

Is there such a thing as a mathematical thesaurus?

I want this for two reasons: When writing proofs, I am constantly in need of synonyms of basic words like thus, there exists, for all, such as, contains, etc. A lot of mathematical concepts have ...
1
vote
1answer
98 views

Name of $a*b=c$ and $b*a=-c$

$A_+=(A,+,0,-)$ is a noncommutative group where inverse elements are $-a$ $A_*=(A,*)$ is not associative and is not commutative $\mathbf A=(A,+,*)$ is a structure where 1) if $a*b=c$ then $b*a=-c$ ...
2
votes
1answer
38 views

a random process model which I do not know the name of

My friend explained to me the following model which comes psychology. I am fairly certain there must be mathematicians who study this type of thing because on its own right it is a very interesting ...
2
votes
1answer
140 views

What does “lifted action” mean?

I read about angular moment and linear moment but I don't know what "lifted action" means. Can you explain please? Thanks. :)
2
votes
3answers
116 views

“Interpolation” of polynomials

I'm dealing with a probability problem and I have to understand the following operation on polynomials: let $F$ and $G$ be any two polynomials of variable $p\in [0,1]$ (to be thought of as a Bernoulli ...
2
votes
0answers
93 views

What is the correct technical term for this generalization of an integer partition?

Given a vector $v$ with non-negative integer coordinates, is there a technical term for an unordered tuple of vectors $(v_1,\dots, v_k)$ with non-negative integer coordinates such that $v_1+\dots+v_k ...
5
votes
1answer
70 views

A prime poset of ideals

Let $A$ be a ring (commutative unital), and $\mathcal I$ be a nonempty family of proper ideals of $A$. I will say that $\mathcal I$ has property $\dagger$ if for any $\mathfrak a\in\mathcal I$ and ...
3
votes
1answer
124 views

Where does ergodic come from?

In math you usually understand why terms such as triangle, function, polynomial, category or even vector. However where does the word ergodic come from? Does it have a meaning in another language? ...