On the duals of the Fibonacci and Catalan-Fibonacci polynomials and Motzkin paths

2021/01/25 by Barry, Paul
#11C20 #15B36 #Combinatorics (math.CO) #FOS: Mathematics #Primary 11B39 #Secondary 11B83

paper · doi:10.48550/arxiv.2101.10218

Abstract

We use the inversion of coefficient arrays to define dual polynomials to the Fibonacci and Catalan-Fibonacci polynomials, and we explore the properties of these new polynomials sequences. Many of the arrays involved are Riordan arrays. Direct links to the counting of Motzkin paths by different statistics emerge.

Related

• Riordan arrays, Chebyshev polynomials, Fibonacci bases
• Walking in the OEIS: From Motzkin numbers to Fibonacci numbers. The "shadows" of Motzkin numbers
• d-orthogonal polynomials, Fuss-Catalan matrices and lattice paths
• Fibonacci-Like Polynomials Produced by m-ary Huffman Codes for Absolutely Ordered Sequences
• Chebyshev Polynomials, Sliding Columns, and the k-step Fibonacci Numbers