2
votes
0answers
25 views

what does “modular” mean?

I find some similarity of the concept "modular set functions" to the cardinality function. But I don't see the cardinality function is also called "modular" or something else. I wonder what "modular" ...
1
vote
0answers
20 views

What does “modular” in “modulr functions” mean?

From Wikipedia If $\Omega$ is a set, a submodular function is a set function $f:2^{\Omega}\rightarrow \mathbb{R}$, where $2^\Omega$ denotes the power set of $\Omega$, which satisfies one of the ...
2
votes
1answer
42 views

How many contiguous subsets of size $N$ does an infinite grid have?

Suppose I have an infinite grid. How many sets of grid points are there that contain $N$ contiguous grid points, and include the grid point at the origin? So for example, if $N$ = 2, then there are 4 ...
2
votes
1answer
20 views

Corrective terms for combinations

Take: $12$ people need to be split up into equal teams for a quiz. How many ways can this be done? The answer may initially seem to be $\displaystyle \frac{12!}{6!6!}$. but, since a single grouping ...
2
votes
2answers
19 views

What's the name of the minimum number of transpositions required to build a permutation?

What's the name of the minimum number of transpositions required to build a permutation? I thought it was "rank" but apparently "rank" refers to the lexicographic number.
1
vote
0answers
128 views

“Dual cardinality” in the graphs $(V_\alpha,\in_\alpha)$

04-25-2014 Enriched with more details Let define the graphs $(V_\alpha,\in_\alpha)$ in $ZFC$ $V_\alpha$ can be finite too $\in_\alpha \subseteq V_\alpha \times V_\alpha$ and ...
0
votes
2answers
60 views

What subject in mathematics investigates the type of problems that constitute the LSAT “logic games” (example given)?

For my own curiosity, I read part of an LSAT study guide yesterday. The "logic games" section comprised questions like, An advertising executive must schedule the advertising during a particular ...
2
votes
1answer
60 views

How did the Symmetric group and Alternating group come to be named as such?

The Dihedral group makes sense, "Di" means two, and "hedral" means.. shape I think (I've just realised how much of what I think words mean are guesses based on experience) like a "polygon" is a 2d ...
11
votes
1answer
193 views

What's the name of this quantity?

For each permutation $\sigma$ of $ \left\{ 1, 2, \dots, n \right\}$ define $$\operatorname{dist}(\sigma)=\sum_{i=1}^{n}\left| \sigma (i)-i \right|$$ For each $n\in\mathbb{N}$, I'm interested in ...
0
votes
1answer
49 views

The name of certain permutations.

The permutations I'm looking at are 2341, 2413, 3412, 3421, 4123 and 4312. I'll explain the property with the example 2413: I start with the first digit (2) and go to the position 2. There I see the ...
1
vote
3answers
155 views

“Set of all formal products” - what does this mean?

List the set of all formal products of $(1+x^2+x^4)^2(1+x+x^2)^2$ with exponents summing to $4$. What is this question asking exactly? What is a "formal product"? Does it have anything to do with ...
0
votes
0answers
48 views

What is that type of TSP

I'm searching for the name of the TSP-like problem. The basic principal is like it follows: When a city is visited by the salesman, he will came in one point and exit the city in another. The ...
3
votes
1answer
58 views

What is the name of graph problem that ask to select some vertices to see every edges.

I want to place light bulbs on some vertices (each bulb will lit up every edges it connected) where all edges lit up. e.g. suppose I have this simple planar graph, Sufficient vertices to place ...
0
votes
0answers
17 views

Terminology: Ramification point

What does a ramification point mean in combinatorics? Is it the same as a branching point?
2
votes
0answers
92 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 ...
1
vote
2answers
137 views

How is this equation called?

I'm trying to figure out some math problems. In particular I have this "In an office you have 6 clerks. How many ways can you select a team of 3 clerks?" and the solution given is: $$\binom{6}{3} = ...
0
votes
0answers
58 views

Abbreviations in Combinatorial Graph/Matrix theory

I'm getting started with research in combinatorics. I have come across a reference that uses a great deal of abbreviations. I was able to figure most of them out but there are a few that I can find. ...
5
votes
1answer
171 views

Extending a partial order to antichains

Let $(S, \leq)$ be a partial order. Let $T$ be the set of antichains of $S$ (i.e., subsets of $S$ whose elements are pairwise incomparable). Define a relation $\leq'$ on $T$ as follows: for all $A$, ...
2
votes
2answers
42 views

What are the sets of vertices in a proper vertex coloring referred to?

A (proper) vertex coloring of a graph is a labelling of the graph’s vertices with colors such that no two vertices sharing the same edge have the same color. A coloring using at most $k$ colors is ...
2
votes
3answers
754 views

Meaning of counting argument?

Does "counting argument" mean a proof of some statements by counting something? Is "counting argument" same as "double counting"? Or does it include both double counting and bijective proof? I ...
0
votes
1answer
63 views

Combination of n sets that produces a set of n-tuple

Given n sets with 3 elements: $X_i=\{a_i,b_i,c_i\}$ where $\{i\in\mathbb{N}|1\leq i\leq n\}$. How can I define a n-tuple based on combination of this sets that produces the set $S$ with $3^n$ ...
2
votes
1answer
80 views

Is there a word to describe the set of permutations of each member of the powerset of a set?

Just what it says on the tin: For a set, X, is there a word to describe the union of sets of permutations of each member of the powerset of X?
1
vote
1answer
248 views

What are k-cycles?

I came across the following question:If we pick a random permutation of $n$ distinct letters,what is the probability that our permutation has at most $k$ cycles? I am not sure I understand the ...
1
vote
1answer
117 views

simplex and power set

I read the following: Let $M$ be a set. The simplex on $M$ is the set of all subsets of $M$; we denote this by $\Delta_M$. We will sometimes refer to the elements of $M$ as vertices of $\Delta_M$. A ...
3
votes
0answers
113 views

The polynomial where only the terms in the multinomial series where each variable's exponent is $>0$ are kept?

I'm wondering if there's a special polynomial with a name out there with $x_1,x_2,\ldots,x_k$ as variables that's defined like this: $$ \sum_{\substack{i_1>0,i_2>0, \ldots,i_k>0 \\ i_1 ...
3
votes
0answers
67 views

Is there are a name for a simplicial complex that is homotopic to the clique complex of its 1-skeleton?

A hollow octahedron is a nice triangulation of the sphere, because once you know the edges, you know everything. The vertices are obviously the ends of the edges, and the faces are any collection of ...
4
votes
2answers
484 views

How to pronounce “tableaux”?

How do you pronounce Young tableaux? Does it sound just like its singular form?
4
votes
3answers
172 views

Does this generalisation of Latin squares have a name?

I am interested in looking at $n\times n$ tableaux (or matrices) in which (WLOG) each integer in $\{ 1, 2, \ldots, n \}$ occurs exactly $n$ times. This is a generalisation of a Latin (or even ...
2
votes
4answers
125 views

“Down-Closed”, “Down Ideal”, Something Else?

Let $X$ be an a set and let $\mathcal{C}$ be a collection of subsets of $X$ satisfying the following property: If $A$ and $A^\prime$ are subsets of $X$ with $A \in \mathcal{C}$ and $A^\prime ...
7
votes
3answers
747 views

What does it mean to “count (some number) of (some finite set of objects)”?

I'm not a native speaker of English. I usually pride myself of my proficiency, but I think I may be stumped here. My problem arises out of this question, which among other things asked for a ...
1
vote
0answers
93 views

Finite Levenshtein distance?

Is there a standard term for the relation on sequences where two sequences are related iff they have a finite Levenshtein distance, or for the equivalence classes it induces?
0
votes
1answer
169 views

Connected and Disconnected Permutations

Martin Klazar's paper Irreducible and connected permutations (pdf) states: We call a permutation $\pi$ of $[n] = \{1, 2, \ldots, n\}$ disconnected iff there is an interval $I \subset [n]$, $2 ...
2
votes
1answer
128 views

What is the name of this special type of n-tuple?

Consider the set, $S$, of $n$-tuples defined inductively as follows: $(1, 2, \ldots, n) \in S$ if $(x_1, x_2, \ldots, x_i, x_{i+1}, \ldots, x_n) \in S$, then $(x_{i+1}, \ldots, x_{n}, x_1, x_2, ...
2
votes
4answers
169 views

Is this a kind of Permutation?

I'm trying to design an algorithm to generate something that I don't know how exactly to call! Ok, I'm not a mathematician, I'm studying computer science and thought this would be a great moment to ...
1
vote
1answer
91 views

Does the term Row-Complete have any synonyms?

I'm wondering if there is other terminology that describes row-completeness, outside the context of a latin square, or if row-complete is actually a general term.
10
votes
2answers
1k views

Why the name 'FACTORIAL'?

Factorial is defined as $n! = n(n-1)(n-2)\cdots 1$ But why mathematicians named this thing as FACTORIAL? Has it got something to do with factors?