Non-Crossing Matchings in the Annulus
Arts and Sciences
The Catalan numbers are a sequence of integers that count various recursively-defined objects, as well as many structures that are important in mathematics and computer science. It is well known that the number of distinct non-crossing matchings on 2n points in the half-plane equals the nth Catalan number. Our work generalizes this notion of non-crossing matchings, as well as the circular matching of Golbach and Tijdeman, to non-crossing matchings in the annulus. We present results enumerating these annular matchings. We also develop interesting bijections between specific classes of annular matchings and well-studied mathematical objects such as combinatorial necklaces and planar graphs.
Pongtanapaisan, Puttipong, "Non-Crossing Matchings in the Annulus" (2015). Symposium on Undergraduate Research and Creative Expression (SOURCE). 429.