## Abstract

We study compositions (ordered partitions) of n. More particularly, our focus is on the bargraph representation of compositions which include or avoid squares of size s × s. We also extend the definition of a Durfee square (studied in integer partitions) to be the largest square which lies on the base of the bargraph representation of a composition (i.e., is 'grounded'). Via generating functions and asymptotic analysis, we consider compositions of n whose Durfee squares are of size less than s × s. This is followed by a section on the total and average number of grounded s × s squares. We then count the number of Durfee squares in compositions of n.

Original language | English |
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Pages (from-to) | 359-367 |

Number of pages | 9 |

Journal | Discrete Mathematics and Applications |

Volume | 28 |

Issue number | 6 |

DOIs | |

State | Published - 1 Dec 2018 |

### Bibliographical note

Publisher Copyright:© 2018 Walter de Gruyter GmbH, Berlin/Boston.

## Keywords

- Durfee square
- composition
- generating function

## ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Applied Mathematics