Algebraic characteristic sets of matroids

Algebraic characteristic sets of matroids

For a matroid M, define the algebraic characteristic set x4(M) to be the set of field characteristics over which M can be algebraically represented. We construct many examples of rank three matroids with finite, non-singleton algebraic characteristic sets. We also determine x,,(PG(Z, p)) and xa(AG(2, p)). An infinite family of rank three matroids with empty algebraic characteristic set is const...

Rough Sets and Matroids

We prove the recent result of Liu and Zhu [2] and discuss some consequences of that and related facts for the development of rough set theory.

Characteristic numbers of algebraic varieties.

A rational linear combination of Chern numbers is an oriented diffeomorphism invariant of smooth complex projective varieties if and only if it is a linear combination of the Euler and Pontryagin numbers. In dimension at least 3, only multiples of the top Chern number, which is the Euler characteristic, are invariant under diffeomorphisms that are not necessarily orientation preserving. In the ...

Some characteristics of matroids through rough sets

At present, practical application and theoretical discussion of rough sets are two hot problems in computer science. The core concepts of rough set theory are upper and lower approximation operators based on equivalence relations. Matroid, as a branch of mathematics, is a structure that generalizes linear independence in vector spaces. Further, matroid theory borrows extensively from the termin...

Learning Families of Closed Sets in Matroids