2014/05/06 by Lisa Seung-Yeon Lee, Lee, Lisa Seung-Yeon
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #math.CO
paper · pdf · doi:10.48550/arxiv.1405.1313
Junior-year thesis at Princeton University
arxiv created 2015/12/01 · arxiv updated 2015/12/02
In this paper, we investigate the importance of column scaling in relating two signed-graphic representations of the same matroid. We used the Sage Mathematics software to generate many examples of signed-graphic matroids and their signed-graphic representations. Our examples show that column scaling is sometimes necessary in order to transform one signed-graphic representation into another; moreover, there exist many collections of signed-graphic representations that row-reduce to the same standard form. We also discuss an interesting matroid-preserving operation on a signed graph, which we call the cylinder flip, that relates certain pairs of signed-graphic representations of the same matroid.