Compositions as non-alternating sequences of partitions

Aubrey Blecher, Charlotte Brennan, Toufik Mansour

Research output: Contribution to journalArticlepeer-review


Compositions are conceptualized as non alternating sequences of blocks of non-decreasing and strictly decreasing partitions. We find the generating function F(x, y, q) where x marks the size of the composition, y the number of parts and q the number of such partition blocks minus 1. We form these blocks starting on the left-hand-side of the composition and maximizing the size of each block. We also find the generating function for the total number of such blocks.

Original languageEnglish
Pages (from-to)211-224
Number of pages14
JournalApplicable Analysis and Discrete Mathematics
Issue number2
StatePublished - 2013


  • Compositions
  • Generating functions
  • Partitions

All Science Journal Classification (ASJC) codes

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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