Catalan triangles and tied arc diagrams
Francesca Aicardi
TL;DR
This paper explores the combinatorial properties of Catalan and Fuss-Catalan triangles through the enumeration of tied arc diagrams, providing new insights into their structural characteristics.
Contribution
It introduces a novel combinatorial framework linking tied arc diagrams to Catalan and Fuss-Catalan triangles, establishing new properties and counting formulas.
Findings
Proved combinatorial properties of Catalan and Fuss-Catalan triangles.
Established a counting method for tied arc diagrams.
Connected tied arc diagrams to well-known combinatorial triangles.
Abstract
The Catalan triangle, as well as a Fuss-Catalan triangle, enter a problem of counting particular tied arc diagrams. This setting allows us to prove some combinatorial properties of these triangles.
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 · Mathematical Dynamics and Fractals · semigroups and automata theory