A matroid is a fundamental and actively studied object in combinatorics. Matroids generalize linear dependency in vector spaces as well as many aspects of graph theory. Moreover, matroids form a cornerstone of tropical geometry and a deep link between algebraic geometry and combinatorics. In this chapter we present OSCAR functions for matroids through several examples. Our focus lies in particular on computing the realization space and the Chow ring of a matroid.

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Matroids

  • Daniel Corey,
  • Lukas Kühne,
  • Benjamin Schröter

摘要

A matroid is a fundamental and actively studied object in combinatorics. Matroids generalize linear dependency in vector spaces as well as many aspects of graph theory. Moreover, matroids form a cornerstone of tropical geometry and a deep link between algebraic geometry and combinatorics. In this chapter we present OSCAR functions for matroids through several examples. Our focus lies in particular on computing the realization space and the Chow ring of a matroid.