Inverses of Motzkin and Schr\"oder Paths
Heinrich Niederhausen
TL;DR
This paper explores the inverses of Motzkin and Schr"oder path matrices, applying them to analyze Hankel determinants and path counting within a horizontal band, revealing new combinatorial insights.
Contribution
It introduces three applications of the inverse matrices, connecting them to path enumeration and determinant calculations, which are novel in this context.
Findings
Inverse Motzkin matrix related to Hankel determinants
Counting paths inside a horizontal band using inverse matrices
Inverse Schr"oder matrix for paths ending on the top side of the band
Abstract
We suggest three applications for the inverses: For the inverse Motzkin matrix we look at Hankel determinants, and counting the paths inside a horizontal band, and for the inverse Schr\"oder matrix we look at the paths inside the same band, but ending on the top side of the band.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Combinatorial Mathematics · Topological and Geometric Data Analysis · Random Matrices and Applications