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Statistics on Linear Chord Diagrams
2019
Discrete Mathematics & Theoretical Computer Science
Linear chord diagrams are partitions of $\left[2n\right]$ into $n$ blocks of size two called chords. We refer to a block of the form $\{i,i+1\}$ as a short chord. In this paper, we study the distribution of the number of short chords on the set of linear chord diagrams, as a generalization of the Narayana distribution obtained when restricted to the set of noncrossing linear chord diagrams. We provide a combinatorial proof that this distribution is unimodal and has an expected value of one. We
doi:10.23638/dmtcs-21-2-11
fatcat:xyuc74ia5fhvtjkbcmlzvjhmje