论文标题
$ Q $ -MATROID的环状公寓
The Cyclic Flats of a $q$-Matroid
论文作者
论文摘要
在本文中，我们开发了$ Q $ - 摩托病的环状公寓理论。我们表明，循环平面的晶格及其排名唯一决定了$ q $ -MATROID，因此得出了新的$ Q $ -Cryptomormormorphism。 We introduce the notion of $\mathbb{F}_{q^m}$-independence of an $\mathbb{F}_q$-subspace of $\mathbb{F}_q^n$ and we show that $q$-matroids generalize this concept, in the same way that matroids generalize the notion of linear independence of vectors over a given field.
In this paper we develop the theory of cyclic flats of $q$-matroids. We show that the lattice of cyclic flats, together with their ranks, uniquely determines a $q$-matroid and hence derive a new $q$-cryptomorphism. We introduce the notion of $\mathbb{F}_{q^m}$-independence of an $\mathbb{F}_q$-subspace of $\mathbb{F}_q^n$ and we show that $q$-matroids generalize this concept, in the same way that matroids generalize the notion of linear independence of vectors over a given field.
