The cyclic flats of a q-matroid

J Algebr Comb (Dordr). 2024;60(1):97-126. doi: 10.1007/s10801-024-01321-2. Epub 2024 May 9.

ABSTRACT

In this paper we develop the theory of cyclic flats of q-matroids. We show that the cyclic flats, together with their ranks, uniquely determine a q-matroid and hence derive a new q-cryptomorphism. We introduce the notion of $F_{q^m}$ -independence of an $F_q$ -subspace of $F_q^n$ 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.

PMID:39101127 | PMC:PMC11294278 | DOI:10.1007/s10801-024-01321-2