Poset shifted matroids and graphs
Abstract
We generalize the notion of shiftedness in simplicial complexes, matroids, and graphs. Using this generalization, called $P$-shiftedness, we give a condition for a matroid to be transversal in terms of a poset $P$. Our result both generalizes and recovers a similar result that characterizes all shifted matroids as transversal. Moreover, we characterize certain shifted and $P$-shifted simple graphic matroids. We also explore the properties of $P$-shifted graphs and classify certain $P$-shifted graph families.
Collections
- OSU Dissertations [11222]