Computational Combinatorics

Month: July, 2012

An Incomplete List of Computational Techniques

Before I have a chance to populate this blog with detailed introductions to specific techniques, we should first investigate a short list of techniques that I plan to write about. Not only does this provide me with a list of posts to write, but provides you with some keywords to look up if you are in need of a computational method now. As I see it, there are four main types of techniques: Enumerative, Exhaustive, Existence, and Non-Existence.

Read the rest of this entry »

Advertisements

Welcome to the Computational Combinatorics Blog

The internet is full of blogs. This is another. Hopefully, this blog will be something new.

There are many blogs featuring technical content. Specifically, there are blogs that document topics in mathematicscombinatorics, theoretical computer science, computational complexity, and many more. Here, the discussion will be focused on computational combinatorics. I believe that it is far too difficult to discover computational methods for combinatorics, and this blog will make it easier.

I define “computational combinatorics” as the use of algorithms and computers to assist in the discovery and proof of combinatorial theorems. Hence, the problems we investigate are inherently combinatorial, but the tools we discuss are very computational.

I plan on having a few different types of posts on this blog:

  • Introduction to a Computational Technique. These posts will highlight a specific computational technique and discuss how to use the technique as well as previous uses.
  • Announcement of Computational Results. When a new result in combinatorics is published (or made available online) a post will present a high-level description of the results and techniques used in the paper. I plan to write such a post for each of my computational combinatorics papers, but I will also write about other papers I read. If you have a computational combinatorics result that you would like to share, please contact me about writing a guest post (you can also contact me about writing a guest post for any other type of post as well).
  • Tips and Tricks. Not all computational techniques are substantial enough to be included in a final research paper, but these tools should be shared. Typically, these will be short examples of using Sage or other software tools to discover new examples of combinatorial objects. 

As the blog develops, other types of posts will be discovered.

I plan to write a post every two weeks, and hope to write a post every week.