Pattern Recognition on Oriented Matroids

10Tope Committees and Reorientations of Oriented Matroids

Let $K_k^{*}\left(M\right)$ as earlier denote the family of tope committees of size k for a simple oriented matroid := (Et, ), and let $K^{*}\left(M\right):={\displaystyle {\cup }_{1\le k\le \left|T\right|-1}{K}_k^{*}\left(M\right)}$ be the family of all tope committees for .

Recall that the kth component ${\kappa }_k^{*}\left(M\right):=\#K_k^{*}\left(M\right),1\le k\le \left|T\right|/2,$ of a “κ*-vector” ${\kappa }^{*}\left(M\right)\in {\mathbb{N}}^{\left|T\right|/2}$ is by convention the number of committees ...