Ascent sequences and upper triangular matrices containing non-negative integers

Mark Dukes, Robert Parviainen

Research output: Contribution to journalArticlepeer-review

34 Citations (Scopus)
26 Downloads (Pure)


The significance of this paper is the introduction of a bijection from ascent sequences to a class of upper triangular integer-valued matrices. Ascent sequences have been shown to uniquely encode interval orders, Stoimenow matchings, and a class of pattern avoiding permutations. This bijection therefore provides a link between this new class of matrices and the aforementioned combinatorial objects, a main goal of the area of bijective combinatorics. This correspondence has since proved instrumental in solving (multi-statistic) enumeration questions related to these structures.
Original languageEnglish
Article numberR53
Number of pages13
JournalThe Electronic Journal of Combinatorics
Publication statusPublished - 2010


  • ascent squares
  • upper triangular matrices
  • natural statistics


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