Counting staircases in integer compositions

Blecher Aubrey, Mansour Toufik

Research output: Contribution to journalArticlepeer-review


The main theorem establishes the generating function F which counts the number of times the staircase 1+2+3+⋯m+ fits inside an integer composition of n. F = km - qxmy/1-x km-1/(1 - q)x(2 m+1) (y/1-x)m + 1-x-xy/1-x (km - qxmy/1-x km-1). where km = ∑æ=0 m-1 xmj-(2j) (y/1 - x)j. Here x and y respectively track the composition size and number of parts, whilst q tracks the number of such staircases contained.

Original languageEnglish
JournalOnline Journal of Analytic Combinatorics
Issue number11
StatePublished - 2016

Bibliographical note

Publisher Copyright:
© 2016, Department of Computer Science. All rights reserved.


  • Composition
  • Generating function

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics


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