Double Wiring Graph
These are the file associated with the generation of double wiring diagrams ["Braids"] and the resulting graphs.
This is the main program file.
The 'Braid' class and implementation. Braids are stored as a multi-dimensional array.
This is a header that contains general functions that I built for this projects, including the encoding/decoding of braid "names". This is needed to run the program.
Both of these files contain list of minors and the name for that combination. The number represents the number of strings. This is needed to run the program
This is a list of all every edge in the graph of four double string wiring diagrams.
This file just has details about the graph of 5 string double wiring diagrams. A file similar to the 4 string edge list is impossible because the length of the braid names and the number of edges creates a file that is multiple gigabytes in size.
This is a Mathematica notebook that contains a graph of the double wiring diagrams for 4 strings.
Total Positivity Conjecture
These files relate to testing the total positivity conjecture. The basic process is that we would generate Fermat code for each braid, which results in every possible minor being written as a combination of the minors in the current braid. Then each of these would be run through Fermat, which produced Laurent polynomials representing each minor. Finally this output was run through a simple script that searched the files for a minus sign that was not preceded by a ^ symbol [this was to exclude negative exponents from the search.]
This program generates Fermat code for each braid in the 3 or 4 string double wiring diagram graph.
This contains all the files needed by the generateFermat program.
These two .zip files contain the generated Fermat files for every braid in 3 and 4 strings. These are the output of generateFermat.cpp
These are the output files from running the EqnFiles through Fermat. These contain polynomials describing each minor for every braid.