Journal of the
Korean Mathematical Society JKMS

Krogdahl \cite{4} introduced the dependence graph that can be defined naturally for a given independent set in a matroid $M$. We are mainly concerned with the dependence poset $DP(I)$ of a base $I$ of $M$ and we investigate what the jump numbers of the dependence poset of bases in $K_n$ and $K_{m,n}$ are. Also we define the adjacent dependent poset $ADP(I)$ and find the jump number of $ADP(B)$ of a base $B$ of $K_n$.

Keywords: jump number, matroids

MSC numbers: 06A07, 05B35