Durfee squares in compositions

Margaret Archibald, Aubrey Blecher, Charlotte Brennan, Arnold Knopfmacher, Toufik Mansour

Research output: Contribution to journalArticlepeer-review

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 languageAmerican English
Pages (from-to)359-367
Number of pages9
JournalDiscrete Mathematics and Applications
Volume28
Issue number6
DOIs
StatePublished - 1 Dec 2018

Keywords

  • Durfee square
  • composition
  • generating function

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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