A hyperfield $H$ is stringent if $a\boxplus b$ is a singleton unless $a=-b$, for all $a,b\in H$. By a construction of Marc Krasner, each valued field gives rise to a stringent hyperfield. We show that if $H$ is a stringent skew hyperfield, then weak matroids over $H$ are strong matroids over $H$. Also, we present vector axioms for matroids over stringent skew hyperfields which generalize the vector axioms for oriented matroids and valuated matroids
AbstractWe extend the notion of representation of a matroid to algebraic structures that we call ske...
We extend the notion of representation of a matroid to algebraic structures that we call skew partia...
AbstractWe present an elementary proof of the well-known theorem of Edmonds and Fulkerson that a mat...
A hyperfield $H$ is stringent if $a\boxplus b$ is a singleton unless $a=-b$, for all $a,b\in H$. By ...
We show that a field extension $K\subseteq L$ in positive characteristic $p$ and elements $x_e\in L$...
Matroids over tracts (Baker and Bowler, 2017) provide an algebraic framework simultaneously generali...
Baker and Bowler defined a category of algebraic objects called tracts which generalize both partial...
In a recent paper Baker and Bowler introduced matroids over hyperfields, offering a common generaliz...
There exist several theorems which state that when a matroid is representable over distinct fields F...
AbstractΔ-matroids are set systems which arise, e.g., in the study of greedy algorithms. Similarly t...
Matroid theory is the study of abstract properties of linear dependence. A matroid consists of a fin...
AbstractThere exist several theorems which state that when a matroid is representable over distinct ...
We extend the notion of representation of a matroid to algebraic structures that we call skew partia...
htmlabstractWe extend the notion of representation of a matroid to algebraic structures that we call...
Hyperfields are algebraic structures generalizing the concept of an algebraic field. In contrast to ...
AbstractWe extend the notion of representation of a matroid to algebraic structures that we call ske...
We extend the notion of representation of a matroid to algebraic structures that we call skew partia...
AbstractWe present an elementary proof of the well-known theorem of Edmonds and Fulkerson that a mat...
A hyperfield $H$ is stringent if $a\boxplus b$ is a singleton unless $a=-b$, for all $a,b\in H$. By ...
We show that a field extension $K\subseteq L$ in positive characteristic $p$ and elements $x_e\in L$...
Matroids over tracts (Baker and Bowler, 2017) provide an algebraic framework simultaneously generali...
Baker and Bowler defined a category of algebraic objects called tracts which generalize both partial...
In a recent paper Baker and Bowler introduced matroids over hyperfields, offering a common generaliz...
There exist several theorems which state that when a matroid is representable over distinct fields F...
AbstractΔ-matroids are set systems which arise, e.g., in the study of greedy algorithms. Similarly t...
Matroid theory is the study of abstract properties of linear dependence. A matroid consists of a fin...
AbstractThere exist several theorems which state that when a matroid is representable over distinct ...
We extend the notion of representation of a matroid to algebraic structures that we call skew partia...
htmlabstractWe extend the notion of representation of a matroid to algebraic structures that we call...
Hyperfields are algebraic structures generalizing the concept of an algebraic field. In contrast to ...
AbstractWe extend the notion of representation of a matroid to algebraic structures that we call ske...
We extend the notion of representation of a matroid to algebraic structures that we call skew partia...
AbstractWe present an elementary proof of the well-known theorem of Edmonds and Fulkerson that a mat...
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