Dan Gordon

Dan Gordon

The La Jolla Combinatorics Repository

In 1996 I started an online database of coverings designs. Over the years it grew and changed, from static HTML pages for each covering, to a MySQL database using PHP, and its current incarnation using AWS EC2 and RDS instances. Hundreds of researchers have contributed tens of thousands of improved coverings over the years, and I’ve added databases for circulant weighing matrices and several types of difference sets,

After thirty years my databases are being retired. The website will continue to be available for some to-be-determined period, but there will be no more changes after March 1, 2026. The data will remain available; each database will be stored on github, with a mirror at zenodo, as a json file. Python code and a jupyter notebook are provided to facilitate reading and processing the data.

The navigation bar at the top of this page leads to descriptions of each of the combinatorial objects and their databases, but if you just want to go to one, the links are:

Each of these databases is being made available under a CC BY 4.0 license. You are free to share and adapt the data any way you like, as long as you give attribution and indicate what changes have been made.

If you have any issues using one of the databases, or notice any errors or omissions, please contact me at dmgordo at gmail dot com.

Why these combinatorial objects?

The collection of databases may seem random, but aside from covering designs, they are connected. The diagram below illustrates this: difference sets and circulant weighing matrices are both special cases of signed difference sets. Relative difference sets may be constructed by lifting difference sets to a larger group, and circulant weighing matrices may be constructed from relative difference sets. See the pages for each object and the papers referenced there for more details.

---
config:
  theme: 'forest'
---
graph TB
    DS<-->RDS((RDS))
    RDS-->CWM
    subgraph SDS
    DS((DS))
    CWM((CWM))
    end