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.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Mathematical Dynamics and Fractals · semigroups and automata theory
