## Abstract

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 language | English |
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Pages (from-to) | 203-217 |

Number of pages | 15 |

Journal | Proceedings of the Indian Academy of Sciences: Mathematical Sciences |

Volume | 127 |

Issue number | 2 |

DOIs | |

State | Published - 1 Apr 2017 |

## Keywords

- Combinatorial statistic
- Integer compositions
- Level
- Rise

## ASJC Scopus subject areas

- General Mathematics