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Country: United States
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Summarized Content

Hello! It’s been a while. I’ve been busy at my new job writing software, and recently I got the itch to do some math again. Of course, I don’t have time to think de*ply about proofs and theorems, but I do have time to write some fun algorithms. I found a new outlet for me to stay connected to the math community while still primarily writing code: the Small Numbers Project This week, my company had a hackathon where we could essentially have a few days to build whatever we want. I spent my hackathon building algorithms to compute van der Waerden numbers and Szemerédi numbers. I also included script to generate constraint systems that verify for C=1 and C=2. There are a lot more things we could do here, such as summarizing results in Ramsey numbers, anti-van der Waerden numbers with C code, which I used for the backtrack search algorithms. Running SAT solvers and theorem provers is probably easier to do than to compile and run the custom tools I built. However, this is an example of an area where custom algorithms are faster: simple backtrack algorithms (with a little bit of care in pruning the search tree) out-perform the general theorem provers in almost all cases. The one case where Z3 is probably much better than backtracking is the Erdős Discrepancy Problem. I became aware of this problem after staggering 13 GB! After this came out, I worked with an undergraduate student, Daniel Geiselhart, to reproduce their result using the same SAT formulation, but with Z3 instead. Daniel found that the Z3 proof was much smaller! We didn’t end up doing anything with that proof, but I decided to reproduce our work here. The Z3 scripts are included, but I haven’t had time to run the scripts on a machine with enough PLEASE CONTRIBUTE TO THE PROJECT! There are a lot of things that can be added to the project, including summaries of existing work, better descriptions of known numbers, and – most importantly – new numbers! Ramsey numbers are notably missing from the project, but only


Computationalcombinatorics Main Page Content

HTML Tag Content Informative?
Title: Computational Could be improved
Description: Not set Empty
H1: Computational CombinatoricsIs it informative enough?
H3: Announcing the Small Numbers ProjectIs it informative enough?

Other Helpful Websites and Services for Computationalcombinatorics

Internal Pages

/about/:
Title

About | Computational Combinatorics

Description

The Computational Combinatorics blog is edited by Derrick Stolee. I define “computational combinatorics” as the use of algorithms and computers to ist in the discovery and proof of combinatorial theorems. Hence, the problems we investigate and inherently combinatorial, but the tools we discuss are very computational. I plan on having a few different types of posts…

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Computational Combinatorics

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/resources/:
Title

Resources | Computational Combinatorics

Description

This page contains a list of resources to help with computational combinatorics. Please email me if you would like to add something to this list. Online Resources ISGCI: Information System on Graph Cl es and their Inclusions ISGCI is an encyclopaedia of graphcl es with an accompanying a application that helps you to research what's known about…

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Computational Combinatorics

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Resources

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Online Resources

/syllabus/:
Title

Syllabus | Computational Combinatorics

Description

Part of the purpose of this blog is to collect enough information on Computational Combinatorics to develop a graduate course on the subject. This page outlines the syllabus of such a course, and how the posts fit within that syllabus. Preliminaries Ranking and Unranking of Combinations and Permutations Symmetry and Automorphisms Canonical Labelings with nauty…

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Computational Combinatorics

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Syllabus

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Preliminaries

/2018/07/26/announcing-the-small-numbers-project/:
Title

Announcing the Small Numbers Project | Computational Combinatorics

Description

Hello! It's been a while. I've been busy at my new job writing software, and recently I got the itch to do some math again. Of course, I don't have time to think ly about proofs and theorems, but I do have time to write some fun algorithms. I found a new outlet for me…

[censored]

H1

Computational Combinatorics

H3

Announcing the Small Numbers Project

/2015/09/18/the-erdos-discrepancy-problem/:
Title

The Erdős Discrepancy Problem | Computational Combinatorics

Description

Computational combinatorics made a big splash last spring when Konev and Lisista announced their SAT-solver-based proof of the Erdős Discrepancy Problem for constant $latex C=2$. Recently, Le Bras, Gomes, and Selman announced another SAT-based solution for $latex C=3$, but when restricting the sequences to have a special property. I was working on a draft blog…

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Computational Combinatorics

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The Erdős Discrepancy Problem

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