Linear chord diagrams with long chords (Q2411506)

Summary: A linear chord diagram of size \(n\) is a partition of the set \(\{1,2,\dots,2n\}\) into sets of size two, called chords. From a table showing the number of linear chord diagrams of degree \(n\) such that every chord has length at least \(k\), we observe that if we proceed far enough along the diagonals, they are given by a geometric sequence. We prove that this holds for all diagonals, and identify when the effect starts.