All Questions
Tagged with examples co.combinatorics
19
questions
2
votes
1
answer
112
views
A diameter 2 arc-transitive graph whose complement is not arc-transitive?
A graph $G=(V,E)$ is arc-transitive if its symmetry group acts transitively on ordered pairs of adjacent vertices.
In general, the complement of an arc-transitive graph is not arc-transitive.
But I ...
- 11.9k
1
vote
1
answer
143
views
Proofs by Schubert calculus and combinatorics
Do you know some examples proved by two different methods: 1. Schubert calculus, 2. combinatorial method.
- 320
8
votes
3
answers
467
views
Problems and algorithms requiring non-bipartite matching
While the importance of the non-bipartite matching problem itself from an algorithmic and complexity point of view is well known, applications of non-bipartite matching are hard to find.
I did an ...
- 12.5k
4
votes
0
answers
55
views
Looking for a Collection of Examples and Counter Examples for Assumptions about the Properties of Planar Euclidean TSP Instances?
Where can I find example and counter examples to seemingly plausible assumption about the properties of optimal solutions of planar euclidean TSP instances?
The reason for asking is that the ...
- 12.5k
10
votes
2
answers
978
views
Densest Graphs with Unique Perfect Matching
Given a graph $G$ with $n$ vertices, that has a perfect matching $M$, what is the maximal number of edges that $G$ can have without contradicting the uniqueness of $M$?
Are examples of such extremal ...
- 12.5k
1
vote
0
answers
189
views
system with solutions $\{x-a:0\leqslant a\leqslant z-1\}$ [closed]
What must be $F$ there where $0=F(1,x,0)=F(x-0,x,z)=F(x-1,x,z)=F(x-2,x,z)=F(x-3,x,z)=$ $\dots$ $=f(x-z-1,x,z)=0$?
Define $F$ in the domain where a continuous function exists that behaves so for $x\...
2
votes
1
answer
134
views
Images of interval edge coloring
I found out the definition of interval edge colorings, concept put by Kamalian in various papers but could not find a graph depicting an example. Where can I find pictures of explicit examples of ...
- 21
16
votes
8
answers
2k
views
Examples of ubiquitous objects that are hard to find?
I've been wrestling with a certain research problem for a few years now, and I wonder if it's an instance of a more general problem with other important instances. I'll first describe a general ...
6
votes
1
answer
537
views
Generating functions with all non-zero coefficients equal to one
I have been wondering if there are any useful generating functions with all non-zero coefficients equal to one. Obviously, the trivial generating function $\frac{1}{1-x}$ has significant applications, ...
- 1,879
8
votes
4
answers
448
views
Order-independent properties arising naturally in mathematics
The motivation for the following question comes from finite model theory,
but it is not a technical question about this field,
and it is particularly directed at people working in other fields.
It ...
- 81
10
votes
2
answers
639
views
Has there been any application of tensor species?
Joyal's combinatorial species, endofunctors in the category of finite sets with bijections $\mathbf B$ have found numerous applications. One generalisation is given by so-called "tensor species" (...
- 5,473
5
votes
9
answers
2k
views
Examples of two different descriptions of a set that are not obviously equivalent?
I am teaching a course in enumerative combinatorics this semester and one of my students asked for deeper clarification regarding the difference between a "combinatorial" and a "bijective" proof. ...
50
votes
4
answers
5k
views
Difficult examples for Frankl's union-closed conjecture
Frankl's well-known union-closed conjecture states that if F is a finite family of sets that is closed under taking unions (that is, if A and B belong to the family then so does $A\cup B$), then there ...
- 28.5k
6
votes
4
answers
2k
views
Examples of Super-polynomial time algorithmic/induction proofs?
In combinatorics, one can sometimes get an algorithmic proof, which loosely has the following form:
-The proof moves through stages
-An invariant is shown to hold by induction from previous stages
-...
- 1,088
30
votes
8
answers
2k
views
Cryptomorphisms
I am curious to collect examples of equivalent axiomatizations of mathematical structures. The two examples that I have in mind are
Topological Spaces. These can be defined in terms of open sets, ...
46
votes
15
answers
11k
views
Strong induction without a base case
Strong induction proves a sequence of statements $P(0)$, $P(1)$, $\ldots$ by proving the implication
"If $P(m)$ is true for all nonnegative integers $m$ less than $n$, then $P(n)$ is true."
for ...
4
votes
2
answers
319
views
Is there a poset with 0 with countable automorphism group?
Is there a poset P with a unique least element, such that every element is covered by finitely many other elements of P (and P is locally finite -- actually, per David Speyer's example, let's say that ...
- 12.5k
50
votes
12
answers
7k
views
Combinatorial results without known combinatorial proofs
Stanley likes to keep a list of combinatorial results for which there is no known combinatorial proof. For example, until recently I believe the explicit enumeration of the de Brujin sequences fell ...
0
votes
3
answers
233
views
Where to find nice diagrams of trees and other graphs? [closed]
Are there some publicly available, vector format diagrams of trees and other graphs? They aren't hard to make, but they sure do take a lot of time (for me).
- 1,803