Add to ORKGRecently, M.~Baker and N.~Bowler introduced the notion of matroids over hyperfields as a unifying theory of various generalizations of matroids. In this paper we generalize the notion of minors and direct sums from ordinary matroids to matroids over hyperfields. Using this we generalize the classical construction of matroid-minor Hopf algebras to the case of matroids over hyperfields
We introduce the notion of a matroid M over a commutative ring R, assigning to every subset of the g...
We extend the notion of matroid representations by matrices over fields by considering new represent...
The results of this dissertation consist of excluded-minor results for Binary Matroids and excluded-...
Hyperfields are algebraic structures generalizing the concept of an algebraic field. In contrast to ...
AbstractThis paper is an initial inquiry into the structure of the Hopf algebra of matroids with res...
In a recent paper Baker and Bowler introduced matroids over hyperfields, offering a common generaliz...
This paper surveys recent work that is aimed at generalising the results and techniques of the Grap...
Matroids over tracts (Baker and Bowler, 2017) provide an algebraic framework simultaneously generali...
A hyperfield $H$ is stringent if $a\boxplus b$ is a singleton unless $a=-b$, for all $a,b\in H$. By ...
We construct a full embedding of the category of hyperfields into Dress's category of fuzzy rings an...
AbstractA partial fieldPis an algebraic structure that behaves very much like a field except that ad...
This paper gives an informal introduction to structure theory for minor- closed classes of matroids...
Matroids are combinatorial abstractions of hyperplane arrangements, and have been a bridge for fruit...
For many classes of combinatorial structures, such as graphs and matroids, there exists a concept of...
The matroid structure theory of Geelen, Gerards, and Whittle has led to a hypothesis that a highly c...
We introduce the notion of a matroid M over a commutative ring R, assigning to every subset of the g...
We extend the notion of matroid representations by matrices over fields by considering new represent...
The results of this dissertation consist of excluded-minor results for Binary Matroids and excluded-...
Hyperfields are algebraic structures generalizing the concept of an algebraic field. In contrast to ...
AbstractThis paper is an initial inquiry into the structure of the Hopf algebra of matroids with res...
In a recent paper Baker and Bowler introduced matroids over hyperfields, offering a common generaliz...
This paper surveys recent work that is aimed at generalising the results and techniques of the Grap...
Matroids over tracts (Baker and Bowler, 2017) provide an algebraic framework simultaneously generali...
A hyperfield $H$ is stringent if $a\boxplus b$ is a singleton unless $a=-b$, for all $a,b\in H$. By ...
We construct a full embedding of the category of hyperfields into Dress's category of fuzzy rings an...
AbstractA partial fieldPis an algebraic structure that behaves very much like a field except that ad...
This paper gives an informal introduction to structure theory for minor- closed classes of matroids...
Matroids are combinatorial abstractions of hyperplane arrangements, and have been a bridge for fruit...
For many classes of combinatorial structures, such as graphs and matroids, there exists a concept of...
The matroid structure theory of Geelen, Gerards, and Whittle has led to a hypothesis that a highly c...
We introduce the notion of a matroid M over a commutative ring R, assigning to every subset of the g...
We extend the notion of matroid representations by matrices over fields by considering new represent...
The results of this dissertation consist of excluded-minor results for Binary Matroids and excluded-...