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.
|Number of pages||13|
|Journal||The Electronic Journal of Combinatorics|
|Publication status||Published - 2010|
- ascent squares
- upper triangular matrices
- natural statistics