As an undergrad and grad math student I had the great privilege of working with USF faculty Dr. Natasha Jonoska and Dr. Masahico Saito. My work was primarily concerned with certain properties of 4-valent rigid vertex graphs used to model DNA recombination, one example of which is the genera of surfaces that said graphs can be cellularly embedded into.
Publications:
R. Arredondo. Reductions On Double Occurrence Words. Proceedings of the Fourty-fourth Southeastern International Conference on Combinatorics, Graph Theory, and Computing. Congressus Numerantium 218 (2013), 43-56. PreprintSoftware:
Nesting index with reductions - verbose nesting index algorithm implemented in JavaScript with web interface
NestIndex.zip - nesting index algorithm implemented in C for use with command line
genus.zip - program to compute genera of surfaces into which simple 4-valent rigid vertex graphs can be embedded
Tables:
Genus Spectrum for Assembly Graphs without Endpoints
Genus Spectrum for Assembly Graphs with Endpoints
Related Work:
Visit our group's web site at Knot.math.usf.edu