The Hessenberg matrices and Catalan and its generalized numbers
Jishe Feng
TL;DR
This paper provides determinantal formulas for Catalan, k-Fuss-Catalan, and generalized numbers using Hessenberg matrices with entries based on binomial coefficients related to lattice path enumeration.
Contribution
It introduces new determinantal representations of these combinatorial numbers through Hessenberg matrices, linking algebraic and combinatorial structures.
Findings
Determinantal formulas for Catalan and k-Fuss-Catalan numbers
Hessenberg matrices with binomial coefficient entries
Connection between matrix entries and lattice path enumeration
Abstract
We present determinantal representations of the Catalan numbers, k-Fuss-Catalan numbers, and its generalized number. The entries of the normalized Hessenberg matrices are the binomial coefficients that related with the enumeration of lattice paths.
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 · Advanced Mathematical Theories and Applications · Matrix Theory and Algorithms