Affiliations: Laboratory of Foundational Aspects of Computer Science, Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch, 7701, South Africa, [email protected] | The John Knopfmacher Centre for Applicable Analysis and Number Theory, Department of Mathematics, University of the Witwatersrand, P. O. Wits, 2050, Johannesburg, South Africa, [email protected] | Department of Mathematics, University of Haifa, 31905 Haifa, Israel, [email protected]
Note: [] Address for correspondence: The John Knopfmacher Centre for Applicable Analysis and Number Theory, Department of Mathematics, University of the Witwatersrand, P. O. Wits, 2050, Johannesburg, South Africa
Abstract: In this paper we consider the absolute variation statistics of a composition σ = σ1 ··· σm 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.
