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

1 vote
0 answers
38 views

Name for a polynomial analogy to divided differences

Let $\lbrace(x_0,y_0),(x_1,y_1),\,\dots,\,(x_n,y_n)\ |\ x_i\ne x_j\rbrace\subset\mathbb{R}^2$ Let $P$ and $Q$ be the polynomials that interpolate $\lbrace(x_0,y_0),(x_1,y_1),\,\dots,\,(x_{n-1},y_{n-1} …
Manfred Weis's user avatar
  • 13.2k
2 votes
1 answer
224 views

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 defini …
Manfred Weis's user avatar
  • 13.2k
2 votes
1 answer
123 views

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 …
Manfred Weis's user avatar
  • 13.2k
1 vote
1 answer
130 views

Functions with periodic sequence of derivative-values

Question: is there an established name for the set $\Big\lbrace\ f {\Large\ \boldsymbol{|}}\ f\in C^\infty\quad {\Large\boldsymbol{\land}}\quad \exists\,{k\in\mathbb{N}^+}:\frac{d^{i+k}}{dx^{i+k}}f(x) …
Manfred Weis's user avatar
  • 13.2k
2 votes

Is there a term for the operation of multiplying the product of two matrices by the transpos...

If you rewrite to $\boldsymbol{X}\boldsymbol{A}\boldsymbol{X}^T$ there is an answer here Names for the product will depend on the properties of $\boldsymbol{X}$ and $\boldsymbol{A}$
Manfred Weis's user avatar
  • 13.2k
0 votes
1 answer
44 views

Name for a type of assignment task

given a bipartite graph $G(U,V,E\subseteq U\times V)$ with strictly positive edge-weights; is there an established name for the the task of calculating the lightest spanning subgraph and what is the b …
Manfred Weis's user avatar
  • 13.2k
2 votes
1 answer
257 views

What do shortest-path algorithms actually calculate?

The motivation for this question is a statement about the Bellman-Ford algorithm, that doesn't agree with the definition of what a path in a graph is. On wikipedia's description of the Bellman-Ford Al …
Manfred Weis's user avatar
  • 13.2k
1 vote
0 answers
43 views

Name for point sets with trivial optimal Hamilton cycle

Question: is there an established name for sets of $n$ points in the euclidean plane whose shortest Hamilton cycles consists of the $n$ pairs of points having the $n$ smallest distances? Names for sym …
Manfred Weis's user avatar
  • 13.2k
0 votes
0 answers
54 views

Attached convex "hulls"

Let $\mathcal{P}$ a finite set of points of a Euclidean $\mathbb{E}^n$ and take the union $\mathrm{U}(\mathcal{P})$ of all closed half-spaces defined by $n$ elements of $\mathcal{P}$ that contain only …
Manfred Weis's user avatar
  • 13.2k
0 votes
0 answers
70 views

Looking for a name for a generalization of geometry to graphs

I am pursuing generalizations of planar Euclidean geometry to complete symmetric and weighted graphs, the guiding principle being applicability to the TSP. The operations and tests that are available …
Manfred Weis's user avatar
  • 13.2k
2 votes
1 answer
183 views

Trying to understand "moats"

According to the TSP Gallery moats provide lower bounds for the optimal solution of TSP instances. On the webpage they are depicted as blue rings around red disks, whose radii represent maximal vertex …
Manfred Weis's user avatar
  • 13.2k
2 votes
0 answers
274 views

What is a hull in the most general mathematical sense?

I have implemented an algorithm that filters the edges of simple complete graph with weighted edges according to a criterion that is inspired by elementary planar geometry and, to my surprise, in the …
Manfred Weis's user avatar
  • 13.2k
2 votes
0 answers
73 views

Distorted elementary functions

Let $f(x)$ be an elementary function defined on $X\subseteq\mathbb{R}$ and $\xi(x), \eta(y)$ strictly monotone for $x\in X,\, y\in f(x)$. Questions: is there an established name for functions of the …
Manfred Weis's user avatar
  • 13.2k
3 votes
1 answer
316 views

Name and properties of $\mathrm{lcm}(\{1,\,\cdots,\,n\})$ [closed]

one of the most prominent functions of the first $n$ natural numbers is the factorial $n!$ that denotes their product. Today however I wondered whether the least common multiple $\mathrm{lcm}(n):=\mat …
Manfred Weis's user avatar
  • 13.2k
6 votes
1 answer
259 views

Name for a matrices having a specific property

is there an established name for the property that a square matrix can be made symmetric by permutation of its columns? Is it possible to recognize those kind of matrices efficiently?
Manfred Weis's user avatar
  • 13.2k

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