# Tagged Questions

**14**

votes

**1**answer

1k views

### What have simplicial complexes ever done for graph theory?

(I am asking in a somewhat tongue-in-cheek fashion, of course, but nevertheless...)
Are there examples of results in "classical" [*] graph theory that have
been achieved by using simplicial ...

**4**

votes

**4**answers

308 views

### Determine if a graph has a large clique

This question is quite specific and practical. I hope it is still relevant for MO and will not be removed.
I have a collection $\mathcal{C}$ of graphs having from 5000-6000 vertices and edge density ...

**4**

votes

**1**answer

175 views

### An intutive reason why a “distance” metric may be a poor one for a procedure where we attempt to modify a string (mutating 0 OR 1 bits)

If I'm attempting to mutate one arbitrarily chosen binary string $s_a$, to another arbitrarily chosen binary string $s_b$, in the smallest number of steps (i.e. with the smallest number of mutations) ...

**4**

votes

**1**answer

393 views

### a conjecture in sum-free sets

Let $ A $ be a set of non-zero integers. Then $A$ contains a sum-free subset $B$ of size $ |B|> \frac{|A|}{3} $ (a result of Erdős). It is conjectured that RHS can be improved to $\frac{|A|}{3} ...

**2**

votes

**5**answers

245 views

### Equivalence relations not associated with a group

This is a vague question; so vague that I wonder if anyone will get it. Many, perhaps most, equivalence relations that are regularly used in mathematics correspond to the orbits of some group action ...

**6**

votes

**2**answers

1k views

### Two questions about combinatorics journals

Hello,
I have two questions regarding combinatorics journals. I hope that this is the right place for such questions.
Which combinatorics/DM journals would you consider as the "top tier"?
I tried ...

**23**

votes

**9**answers

2k views

### Is the empty graph a tree?

This is a boring, technical question that I stumbled upon while making a contribution to Sage. I would still like to hear a constructive answer so hopefully the question does not get closed.
The ...

**6**

votes

**4**answers

841 views

### fourier analytic proofs

While searching through Mathoverflow, I found out a fourier analytic proof of the Isoperimetric Inequality.Also, by google search I found a fourier analytic proof of Quadratic Reciprocity theorem.I ...

**7**

votes

**3**answers

498 views

### Intuition Behind a Decimal Representation with Catalan Numbers

From $0 = 0.5 - 0.5 = 0.5 - \sqrt{0.25}$, we can adjust the subtrahend slightly to obtain
$$0.5 - \sqrt{0.249} = 0.001\ 001\ 002\ 005\ 014\ 042\ldots$$
where the decimal representation contains the ...

**13**

votes

**0**answers

772 views

### Origins of the Nerve Theorem

Recently, I've read two papers which have cited the Nerve Theorem, one crediting Borsuk with the result and another Leray. Here is the question:
Who was the first to prove the Nerve Theorem?

**17**

votes

**6**answers

2k views

### True by accident (and therefore not amenable to proof)

The graph reconstruction conjecture claims that (barring trivial examples) a graph on n vertices is determined (up to isomorphism) by its collection of (n-1)-vertex induced subgraphs (again up to ...

**3**

votes

**2**answers

548 views

### Open problems and known identities involving sums

As many people here, I know of a few identities involving expressions of the type $\sum_{i}\ f(i)$, with "arbitrarily complicated $f(\cdot)$", as well as closed formulas in some cases.
I also know ...

**9**

votes

**4**answers

2k views

### A learning roadmap for Additive combinatorics.

Hello,
I'd love to learn more about the field of additive combinatorics. From what I've understand, there's a book by Tao and Vu out on the subject, and it looks fun, but I think I lack the ...

**16**

votes

**4**answers

661 views

### Arrow's theorem and the postseason

There are a number of instances of sports teams intentionally losing matches in order to secure a more favorable situation in a playoff round. While this doesn't happen terribly often, when it does ...

**9**

votes

**2**answers

622 views

### Advantageous properties of 4 letter alphabet (in DNA)?

As you know DNA is composed of strings of 4 letters. I am wondering if the number 4 here has
any significance? Any property of 4 that makes using 4 letters more advantageous over more
(or less) ...

**5**

votes

**3**answers

253 views

### Medium-Sized Calculations and Organization

This is not a math question as much as a process question. For the first time in my (very short) career, I find myself doing one of those messy calculations, where each 'line' of the calculation can ...

**8**

votes

**4**answers

1k views

### the delta system lemma outside set theory

The lemma:
Any uncountable set $S$ of finite sets has an uncountable subset $\Delta \subseteq S$ and an $x$ such that $\forall a,b \in \Delta$, if $a \neq b$ then $a \cap b = x$. $\Delta$ is called a ...

**3**

votes

**9**answers

1k views

### Are there any important mathematical concepts without discrete analog?

In "continuous" mathematics there are several important notions such as covering space, fibre bundle, Morse theory, simplicial complex, differential equation, real numbers, real projective plane, etc. ...

**31**

votes

**5**answers

2k views

### Why do wedges of spheres often appear in combinatorics?

Robin Forman writes in "A User's Guide to Discrete Morse Theory":
The reader should not get the
impression that the homotopy type of a
CW complex is determined by the number
of cells of each ...

**14**

votes

**11**answers

6k views

### Different ways of proving that two sets are equal

I'm not sure if this is a soft question, or should be community wiki.
I was explaining to a student how to prove that two sets were equal using what I called the 'oldest trick in the book': to show ...

**4**

votes

**1**answer

1k views

### Combinatorics journals processing time

This is a spin-off question from How to select a journal?. Is there is any data available regarding processing time (acceptance time, time from submission to publication, or similar) specifically for ...

**21**

votes

**6**answers

5k views

### Submitting to arXiv when unaffiliated

I am writing a short paper in the area of combinatorics.
When the paper is complete, I would like to be able to submit it to arXiv.
The reasons that I would like to submit to arXiv are:
To obtain ...

**5**

votes

**2**answers

1k views

### Yet another graph invariant: the similarity matrix

Preliminaries
Let $n \in \mathbb{N}$ and $v$ be a vertex of a graph $G$. Let the $n$-neighbourhood of $v$, $N_n(v)$, be the induced subgraph of $G$ containing $v$ and all vertices at most $n$ edges ...

**11**

votes

**8**answers

28k views

### The factorial of -1, -2, -3, …

Well, n! is for integer n < 0 not defined -- as yet.
So the question is: How could a sensible generalization of the factorial for negative integers look like?
Clearly a good generalization should ...

**8**

votes

**10**answers

775 views

### Algorithmic Combinatorics resources?

Some branches of combinatorics lend themselves naturally to algorithms; graph theory is a natural example. However, straight-up enumerative combinatorics relies much more on analytic and algebraic ...

**8**

votes

**3**answers

526 views

### “Plateaus” to watch out for

I'm a lot earlier in my math education that most of the people on this site. Currently I'm studying computer science, and I'm interested in looking into statistical and optimization applications, as ...