d-orthogonal polynomials, Fuss-Catalan matrices and lattice paths

2025/05/22 by Paul Barry, Barry, Paul
Computer Science · Materials Science · Mathematics · #11B37 #11B83 #11C20 #11Y55 #11Y55 11C20 #42C05 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Primary 05A15 #Quasicrystal Structures and Properties #Secondary 15B36 #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2505.16718

openalex publication_date 2025/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note, we show how to define certain Riordan arrays, that we call the Fuss-Catalan-Riordan arrays, by means of a special family of d-orthogonal polynomials. We relate the Fuss-Catalan Riordan arrays to the Fuss Catalan numbers, and to certain lattice paths. We emphasise the role of the production matrices of the Riordan arrays that we encounter in our study.

Citations

• Catalan-Spitzer permutations
• The On-Line Encyclopedia of Integer Sequences

Related

• Notes on Riordan arrays and lattice paths
• Characterizations of the Borel triangle and Borel polynomials
• On Some Alternative Characterizations of Riordan Arrays
• Riordan arrays, Chebyshev polynomials, Fibonacci bases
• A Riordan array family for some integrable lattice models