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
AbstractΔ-matroids are set systems which arise, e.g., in the study of greedy algorithms. Similarly t...
We show that each algebraic representation of a matroid M in positive characteristic determines a ma...
Bodlaender et al. [7] proved a converse to Courcelle's Theorem for graphs [15] for the class of chor...
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 $x_e\in L$...
Baker and Bowler defined a category of algebraic objects called tracts which generalize both partial...
Matroids over tracts (Baker and Bowler, 2017) provide an algebraic framework simultaneously generali...
Recently, M.~Baker and N.~Bowler introduced the notion of matroids over hyperfields as a unifying th...
We construct a full embedding of the category of hyperfields into Dress's category of fuzzy rings an...
In a recent paper Baker and Bowler introduced matroids over hyperfields, offering a common generaliz...
We extend the notion of representation of a matroid to algebraic structures that we call skew partia...
We extend the notion of matroid representations by matrices over fields by considering new represent...
Hyperfields are algebraic structures generalizing the concept of an algebraic field. In contrast to ...
Matroid theory is the study of abstract properties of linear dependence. A matroid consists of a fin...
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...
We show that each algebraic representation of a matroid M in positive characteristic determines a ma...
Bodlaender et al. [7] proved a converse to Courcelle's Theorem for graphs [15] for the class of chor...
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 $x_e\in L$...
Baker and Bowler defined a category of algebraic objects called tracts which generalize both partial...
Matroids over tracts (Baker and Bowler, 2017) provide an algebraic framework simultaneously generali...
Recently, M.~Baker and N.~Bowler introduced the notion of matroids over hyperfields as a unifying th...
We construct a full embedding of the category of hyperfields into Dress's category of fuzzy rings an...
In a recent paper Baker and Bowler introduced matroids over hyperfields, offering a common generaliz...
We extend the notion of representation of a matroid to algebraic structures that we call skew partia...
We extend the notion of matroid representations by matrices over fields by considering new represent...
Hyperfields are algebraic structures generalizing the concept of an algebraic field. In contrast to ...
Matroid theory is the study of abstract properties of linear dependence. A matroid consists of a fin...
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...
We show that each algebraic representation of a matroid M in positive characteristic determines a ma...
Bodlaender et al. [7] proved a converse to Courcelle's Theorem for graphs [15] for the class of chor...
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