Abstract. Our main result describes how to extend a matroid so that its ground set is a modular hyperplane of the larger matroid. This result yields.

Our main result describes how to extend a matroid so that its ground set is a modular hyperplane of the larger matroid. This result yields a new way to view ...

Our main result describes how to extend a matroid so that its ground set is a modular hyperplane of the larger matroid. This result yields a new way to view ...

Jun 19, 2020 · The matroid of circuits of a matroid M with a representation as a multiset of vectors can be defined as the cocircuit matroid of the dual M ⊥ with an ...

A certain result known for cycles and cocycles in graphs is extended to matroids. It is shown that for a k-connected regular matroid having circumference c ...

Sep 23, 2023 · My idea for solving this question is that, given a circuit C, subtract from it an element x, then C−x∈I(M) which is the set of independent sets ...

a cocircuit in a matroid cannot have exactly one common element, while a matroid ... that each matroid in the sequence is a lift or an extension of its ...

We extend this result to matroids.Call a cocircuit of a matroid M short if its size is at most the rank of M. Then we prove that for any simple binary matroid ...

Oct 11, 2017 · A regular matroid can be thought of, rather imprecisely, as the smallest natural class of objects which contain graphs and admit a duality ...

Apr 7, 2019 · In this work, we extend this construction to general oriented matroids and circuit (respectively, cocircuit) signatures coming from generic.