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Variation Statistics on Compositions

Archibald M., Knopfmacher A., Mansour T.

Fundamenta Informaticae

2012

Vol. 117, nr 1-4

1-17

In this paper we consider the absolute variation statistics of a compositionσ=σ_1...σ_m of n which is a measure of the sum of absolute differences between each consecutive pair of parts in a composition. This and some related statistics which we discuss, can also be interpreted within the context of bargraph polygons and bargraph walks of area n. In this context, absolute variation corresponds to the interior vertical perimeter of a bargraph polygon or to the interior vertical length of a bargraph walk.