Pattern Recognition on Oriented Matroids

12Critical Committees and Distance Signals

If $\mathfrak{V}$ is the vertex sequence of some path in a connected graph, then the corresponding sequence (d(w, v): v ∈ ) of the distances between its vertices and distinguished vertex w of the graph can be extended in a natural way to a periodic signal.

In this chapter we consider such distance signals associated with symmetric cycles in the tope graph of a simple oriented matroid. When the vertex sequence of a symmetric cycle is regarded as a subposet of the tope poset, and the distinguished vertex of the tope graph is the base tope of the tope poset, a few basic properties of the discrete Fourier transform ...