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Set functions satisfying if $f(X) \le f(Y)$ and $Z \cap (X \cup Y) = \emptyset$, then $f(X \cup Z) \le f(Y \cup Z)$

I am investigating set functions $f : 2^\Omega \to \mathbb{N}$ satisfying the following two properties: (monotone) For all $X, Y \subset \Omega$, if $X \subseteq Y$, then $f(X) \le f(Y)$. (property ...
Glenn Sun's user avatar
  • 151
8 votes
1 answer
403 views

Smallest relation in complement of partial order that prohibits its extension

Let $P$ be a partial order on a finite set $S$ (assume that every element is related to at least one other element besides itself…this raises a few quick questions: is this implied by the definition ...
mathematrucker's user avatar
2 votes
1 answer
777 views

Is there a term for a subgraph which includes all the edges of a graph?

A subgraph is called spanning when it includes all of the vertices of the given graph. Is there a term for a subgraph which includes all the edges of a graph? Thanks.
Tim's user avatar
  • 357
1 vote
1 answer
102 views

How do I fit flow values to connections in a known network?

This is not my area and I'm new to its terminology, and am posting my problem in the hope that someone will be able to direct me to where it has been solved, or who has written about it. I have a flow ...
hmkc's user avatar
  • 11
8 votes
0 answers
176 views

Does the "coproduct-elimination transform" have an accepted name, and where can I learn more about it?

Suppose we're in a bicartesian closed category. Then given a morphism $$f : X \rightarrow Y_1 + \ldots + Y_n$$ and a test object $T$, we get a corresponding morphism $$T^f : X \times [Y_1,T] \times \...
goblin GONE's user avatar
  • 3,793
4 votes
0 answers
140 views

Is there any accepted single-word that means "partial function"?

When I'm explaining things involving partial functions, I usually end up stumbling over my words, like so: "Suppose $f : A \rightarrow B$ is a function, uhh, sorry I mean a partial function, and ...
goblin GONE's user avatar
  • 3,793
4 votes
1 answer
434 views

Giving the same concept different names in the same paper

I found a seminal paper of renowned authors (Inference of Finite Automata Using Homing Sequences (1993) by Ron Rivest and Robert Schapire) in which the authors define the very same set-theoretic ...
Hans-Peter Stricker's user avatar
4 votes
0 answers
199 views

Correspondence between numerical semigroups and polynomials?

A numerical semigroup $A$ is defined as a subsemigroup of the semigroup $(\mathbb{N},+)$ of the positive integers such that the set $\mathbb{N}\setminus A$ is finite. Equivalently (for a subsemigroup) ...
Miroslav Korbelar's user avatar
1 vote
4 answers
2k views

What is the name of the function f(x,y) = ((x-1) mod y)+1 ?

Does the function $f(x,y) = ((x-1) \mod y)+1$ have an existing name? f(1,5) = 1 f(2,5) = 2 ...
Niall Murphy's user avatar