2
votes
0answers
26 views

What is the motivation behind the study of pattern-avoiding permutations?

There is a ton of research on pattern-avoiding permutations (permutations that do not contain some designated permutation pattern). We're figuring out how to enumerate them, what random ones are ...
1
vote
1answer
57 views

Iterations of Pascal's Identity

Pascal's Identity states that $n \choose k$ = $n-1 \choose k-1$ + $n-1 \choose k$ since if one element is separated from the rest we can claim that either it is chosen (resulting in $k-1$ elements ...
2
votes
1answer
51 views

How many answers can be created using the elementary arithmetic operators?

If I gave you an amount of $n$ numbers, how many anwswer will you be able to create using the elementary arithmetic operators ($+, -, \times, /$)? These are the rules: All numbers ...
7
votes
4answers
270 views

An unexpected application of non-trivial combinatorics

PROBLEM STATEMENT Given two finite sets $A$ and $B$, each containing $s \in \mathbb N$ elements, how many pairs of functions $f \colon A \rightarrow B$ and $g \colon B \rightarrow A$ are there, ...
3
votes
3answers
480 views

Uses of the incidence matrix of a graph

The incidence matrix of a graph is a way to represent the graph. Why go through the trouble of creating this representation of a graph? In other words what are the applications of the incidence matrix ...
17
votes
3answers
750 views

Exceptional books on real world applications of graph theory.

What are some exceptional graph theory books geared explicitly towards real-world applications? I would be interested in both general books on the subject (essentially surveys of applied graph ...
0
votes
1answer
90 views

Blackjack 21 training

A friend of mine has to do An essay on this and I thought this was a great place to ask. In the movie: the main character is seen reading a lot of books which he calls simple arithmetic instead of ...
1
vote
1answer
656 views

Combinations for Screen lock For iPhone / Android

I was wondering if there was a general for formula to calculate the combination of the password lock for the current smart phones The following is the condition We must use four nodes or more to ...
2
votes
3answers
399 views

Applications of the number of spanning trees in graphs

Let $G$ be a simple graph and denote by $\tau(G)$ the number of spanning trees of $G$. There are many results related to $\tau(G)$ for certain types of graphs. For example one of the prettiest (to ...
4
votes
4answers
361 views

How many cpus needed to check a 100 million digit prime number efficiently?

If I had access to potentially large number of CPUs and wanted to quickly check 100 million digit numbers for primality using a map-reduce architecture, how many CPUs would be necessary? Each of the ...
15
votes
16answers
6k views

Applications of the Fibonacci sequence

The Fibonacci sequence is very well known, and is often explained with a story about how many rabbits there are after $n$ generations if they each produce a new pair every generation. Is there any ...