Concave compositions

George E. Andrews

Research output: Contribution to journalArticlepeer-review

30 Scopus citations


Concave compositions are compositions (i.e. ordered partitions) of a number in which the parts decrease up to the middle summand(s) and increase thereafter. Perhaps the most surprising result is for even length, concave compositions where the generating function turns out to be the quotient of two instances of the pentagonal number theorem with variations of sign. The false theta function discoveries also lead to new facts about concatenatable, spiral, self-avoiding walks.

Original languageEnglish (US)
Pages (from-to)1-13
Number of pages13
JournalElectronic Journal of Combinatorics
Issue number2
StatePublished - 2011

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics
  • Applied Mathematics


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