From rankings’ collinearity to counting SDR's via chromatic list expression

Abstract

The problem of counting rankings satisfying the collinearity condition with respect to two rankings over the metric spaces of rank distance is treated in this paper by transforming it into finding the number of systems of distinct representatives (abbreviated as SDR's) with respect to associated set systems. A formula for the chromatic list expression of graphs is then given in terms of the inclusion and exclusion principle, followed by a formula for the number of SDR's of set systems when the graphs are complete.

Keywords:

• rank distance
• collinearity condition
• system of distinct representatives
• L-coloring
• chromatic list expression

2000 AMS Subject Classification :

• 05C15
• 68R15
• 68N30

Acknowledgements

The authors wish to thank the referees for their comments and many helpful suggestions concerning the first version of this paper. The first author is indebted to MEdC-ANCS and PNII-Idei, project number 228, which supported this research.