• Counting rises and levels in $r$-color compositions

    • Fulltext


        Click here to view fulltext PDF

      Permanent link:

    • Keywords


      Combinatorial statistic; integer compositions; rise; level

    • Abstract


      An $r$-color composition of a positive integer $n$ is a sequence of positiveintegers, called parts, summing to n in which each part of size $r$ is assigned one of $r$ possible colors. In this paper, we address the problem of counting the $r$-color compositions having a prescribed number of rises. Formulas for the relevant generating functions are computed which count the compositions in question according to a certain statistic. Furthermore, we find explicit formulas for the total number of rises within all of the $r$-color compositions of $n$ having a fixed number of parts. A similar treatment is given for the problem of counting the number of levels and a further generalization in terms of rises of a particular type is discussed.

    • Author Affiliations



      1. Department of Mathematics, University of Haifa, 31905 Haifa, Israel
    • Dates

  • Proceedings – Mathematical Sciences | News

    • Editorial Note on Continuous Article Publication

      Posted on July 25, 2019

      Click here for Editorial Note on CAP Mode

© 2017-2019 Indian Academy of Sciences, Bengaluru.