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Ascent sequences and upper triangular matrices containing non-negative integers

Dukes, Mark and Parviainen, Robert (2010) Ascent sequences and upper triangular matrices containing non-negative integers. The Electronic Journal of Combinatorics, 17.

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Abstract

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.