2021/04/03 by Keiichi Shigechi, Shigechi, Keiichi
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Mathematical Physics (math-ph) #math-ph #math.CO #math.MP
paper · pdf · doi:10.48550/arxiv.2104.01391
14 pages
arxiv created 2021/04/03 · openalex publication_date 2021/04/03 · arxiv updated 2021/04/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce and study cover-inclusive and cover-exclusive Dyck tilings of type D. It is shown that the generating functions of Dyck tilings of type D are expressed in terms of the generating function of ballot tilings of type B. We introduce link patterns of type D and plane trees for a ballot path, and construct a map from trees to ℤ[q]. This map gives the generating function of cover-inclusive Dyck tilings of type D associated to the ballot path.