All Questions
21 questions
0
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69
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What should we call the area for which the lower border is a Motzkin path?
We can draw a Motzkin path from $(0,0)$ to $(n/2,n/2)$ using steps $(0,1)$, $(1,0)$ and $(1/2,1/2)$, such that the path never goes below the line $y=x$. Consider the area bounded by the Motzkin path, ...
- 135
3
votes
1
answer
181
views
Decomposing a set of integers as a union of well-separated (discrete) intervals
Let a discrete interval be a set of the form $\{x \in \mathbb Z \colon a \le x \le b\}$ with $a, b \in \mathbb Z \cup \{\pm \infty\}$. Then define the boxing dimension $\text{bim}(S)$ of a set $S \...
- 10.5k
1
vote
1
answer
146
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Name for an easy combinatorial game
What is the name of the following combinatorial game:
Two players, moving in turn.
Positions: $0,1,2,\ldots$.
Moves: $n\longmapsto n-1$ or $n\longmapsto \lfloor n/2\rfloor$
if $n>0$.
No move for $0$...
- 17.9k
15
votes
1
answer
724
views
English name and references for a combinatorial puzzle from Japan [closed]
I am looking for the name and references of the following puzzle.
There are n intersecting circles in a row.
At the center of the circle and at the intersection of the two circles, fill the numbers 1, ...
- 151
4
votes
1
answer
182
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Finding a subclass of lattices in the literature
Assume you have an algebraic problem that outputs a list of (finite) lattices on $n$ points for a given number $n$.
Question 1: Is there a way to search the internet/literature to see what exactly ...
- 26.5k
3
votes
1
answer
143
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Reference request: Spectrum of intersection matrices
Let $P(A)$ be the set of all non-empty proper subsets of a finite set $A$. Let $M$ be a matrix indexed by the set in $P(A)$ whose $ij$ the entry is $1$ if the associated sets are disjoint and $0$ ...
- 1,269
1
vote
0
answers
35
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Term or reference for a set of integer edge weights to guarantee distinct weighted degrees
I am looking for a term or reference describing sets $S$ of $\binom{n}{2}$ non-negative integers such that, for every bijection $w: E(K_n)\to S$ and every pair of distinct vertices $u$ and $v$ in $V(...
- 11
4
votes
1
answer
499
views
I want to know the name of or any references for a matrix in the book "The representation theory of the symmetric groups" by Gordon James
$\DeclareMathOperator{\Ind}{\operatorname{Ind}}$I'm reading "The representation theory of the symmetric groups" written by Gordon James.
I found the matrix $B$ in the chapter 6 ("The ...
- 1,013
7
votes
0
answers
74
views
Graphs all of whose cuts are positive
Let $(V, E, w)$ a weighted graph, with vertices $V$, edges $E$, and signed weight $w:E\to \mathbb R$.
I am interested to know other popular properties that are known to imply, or are equivalent to, ...
- 2,041
2
votes
0
answers
124
views
Graphs which are built from complete graphs : Reference request
Let $V$ be a set of $n$ vertices. Fix $3 \le k \le n$. Let $\binom V k$ be the set of all $k$ element subsets of $V$.
We add the edges in $V$ as follows: Let $\mathcal S \subseteq \binom V k$ be ...
- 1,269
1
vote
0
answers
90
views
Is there any name/occurence to this sequence of numbers?
I am curious if there is any name for this sequence of numbers, or any occasion that this sequence is used.
The sequence is $(c_1,c_2,c_3,\cdots)$ with recursive formula
$$c_n=\frac{1}{2n+1}\sum_{i=...
- 323
1
vote
1
answer
156
views
What is a reference for this sort of test set system that avoids all sets of size $\le k$?
My question is: is there a standard name for a structure like the following?
For positive integers $n$, $k < n$ define a "$k$-set-free test for $n$" as a set $C$ of subsets of the integers $\{0, \...
- 77
3
votes
0
answers
346
views
Terminology for transforming a directed acyclic graph into a tree
I am looking for the term of converting a directed acyclic graph (DAG) into a tree by traversing its topologically ordered nodes and copying the subtrees of the nodes with in-degree $> 1$.
Such a ...
- 265
7
votes
2
answers
390
views
On a statistic for permutations
Given a permutation $\pi$ we can write $\pi=s_{i_1} ... s_{i_l}$ as a product of simple transpositions $s_i=(i,i+1)$ in a minimal way.
Question 1: Is there an "official" name for the permutation ...
- 26.5k
3
votes
1
answer
223
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Yet another graph characteristic
I wonder if the following graph-theoretical concepts have been considered before, and if so, under which name.
Consider a directed graph $G$ with $n$ nodes.
Let the cycle number $\gamma(\nu)$ be ...
- 9,720
3
votes
0
answers
92
views
Terminology for set systems: "trace" or "projection"?
Although the following question is not in itself mathematical, it is the expertise/breadth of the research community in mathematics that I wish to appeal to, beyond the filtered/trained search results ...
- 25.8k
1
vote
1
answer
371
views
Basis of cone lattice
I only want to know whether a construction that I use appears in literature and maybe has a name already.
Let $V$ be a $\mathbb Q$ vector space of dimension $d\in\mathbb N$.
A subset $C\subset V$ is ...
user130903
0
votes
0
answers
131
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terminology: monotone maps of posets such that the image of a lower set is a lower set
How are called in combinatorics
monotone maps of partially ordered sets such that the image of a lower set is a lower set, i.e. closed (or open) maps of finite topologies? Is there a classification ...
- 113
5
votes
1
answer
261
views
Is there a standard name for this poset
I've run into the following poset and I would expect it has a standard name. Let $n\geq k\geq 0$. Then $P_{n,k}$ consists of all $k$-element subsets of $\{1,\ldots,n\}$ ordered by $X\leq Y$ if $X=\{...
- 38.6k
3
votes
0
answers
195
views
Is there a name for this property in set-valued analysis?
Consider a set-valued, finite-valued map $F$ from a set $X$ to subsets of $X$. Consider the following property: $|F(x)| \geq |F(y)|$ for all $x,y$ such that $y \in F(x)$.
I have defined this property ...
- 61
10
votes
3
answers
640
views
Seeking reference for the enumerative "mass formula" concept
I am teaching a combinatorics class in which I introduced the notion of a "mass formula". My terminology is inspired by the Smith–Minkowski–Siegel mass formula for the total mass of ...
- 56.6k