Counting rises and levels in r-color compositions

Toufik Mansour, Mark Shattuck

Research output: Contribution to journalArticlepeer-review


An r-color composition of a positive integer n is a sequence of positive integers, called parts, summing to n in which each part of size r is assigned one of r pos- sible 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.

Original languageEnglish
Pages (from-to)203-217
Number of pages15
JournalProceedings of the Indian Academy of Sciences: Mathematical Sciences
Issue number2
StatePublished - 1 Apr 2017


  • Combinatorial statistic
  • Integer compositions
  • Level
  • Rise

ASJC Scopus subject areas

  • General Mathematics


Dive into the research topics of 'Counting rises and levels in r-color compositions'. Together they form a unique fingerprint.

Cite this