Properties of local rank map vectors from multidetection chromatograms

Different windowing techniques estimate the local rank map of a two-dimensional multidetection chromatogram. A rank map vector, however, does not provide an unique determination of the location of components (referred to as the chromatographic configuration). This paper emphasizes on two problems: 1. (1) How many local rank map vectors are allowed and how can they be generated from the knowledge of the number of different components? 2. (2) For a given local rank map vector, how many different chromatographic configurations are possible and how can they be generated? The presented theorems can be useful in the process of determining correct local rank map vectors and chromatographic configurations.