Enumeration of idempotents in planar diagram monoids

The code in this project can be used to count idempotents in the Jones, Motzkin, and Kauffman monoids, and is based on Enumeration of idempotents in planar diagram monoids by Igor Dolinka, James East, Athanasios Evangelou, Desmond FitzGerald, Nicholas Ham, James Hyde, Nicholas Loughlin, and James Mitchell.

Installation

In your terminal of choice, perform the following steps to install this project.

0. Clone this repository by doing

    git clone https://github.com/james-d-mitchell/Jones
   

   This will create a directory called Jones in whatever directory you were in to begin with.

1. Type cd Jones to change directory into the Jones folder created in Step 1.

2. Type

    git clone https://github.com/cassioneri/Dyck
   

   This will create a directory called Dyck inside the directory Jones.

3. Type make which will create executables for the three programs in this project jones, motzkin and kauffman. This project is written in C++11, and so you will require a C++ compiler compatible witht this standard.

You might want to test that everything worked by doing make test which should display

tst/jones.sh
tst/motzkin.sh
tst/kauffman.sh

but nothing further.

Counting idempotents

If n is any positive integer, then jones n returns the number of idempotents in the Jones monoid of degree n. If you want more information about what is going on, then do jones -v n motzkin and kaufmann can be used in the same way.

jones, motzkin, and kauffman are a multi-threaded C++ programs. By default the number of threads used is one less than the maximum supported by the hardware.

You can alter the number of threads by changing the variable nr_threads in the files src/jones.cc, src/kauffman.cc, and/or src/motkzin.cc, and rerunning make. Each of the programs will then use nr_threads + 1 threads, regardless of the maximum number of threads which your hardware supports.

Enjoy!

Copyright (C) 2016-18 James D. Mitchell

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.