Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 1 of 1
Full-Text Articles in Physical Sciences and Mathematics
Free Resolutions Associated To Representable Matroids, Nicholas D. Armenoff
Free Resolutions Associated To Representable Matroids, Nicholas D. Armenoff
Theses and Dissertations--Mathematics
As a matroid is naturally a simplicial complex, one can study its combinatorial properties via the associated Stanley-Reisner ideal and its corresponding free resolution. Using results by Johnsen and Verdure, we prove that a matroid is the dual to a perfect matroid design if and only if its corresponding Stanley-Reisner ideal has a pure free resolution, and, motivated by applications to their generalized Hamming weights, characterize free resolutions corresponding to the vector matroids of the parity check matrices of Reed-Solomon codes and certain BCH codes. Furthermore, using an inductive mapping cone argument, we construct a cellular resolution for the matroid …