Periodic column partial sums in the Riordan array of a polynomial
Abstract
When p(t) is a polynomial of degree d, the k-th column of the Riordan arrayis an eventually periodic sequence whose repeating part begins at the 1+(k-1)(d+1) -st term.The preperiodic terms add up to the (k -1)(d + 1)-st partial sum of the corresponding formal power series, and thus the Riordan array of p(t) generates a sequence of column partial sums.We classify the linear and quadratic polynomials, and present a particular family of polynomials of higher degree, for which these sequences of column partial sums are eventually periodic.
Fields of Study & Subjects
Advanced Combinatorial Mathematics
Graph theory and applications
Analytic Number Theory Research
Publication details
- Journal / source
- Enumerative Combinatorics and Applications
- Publisher
- University of Haifa
- Volume
- 6
- Issue
- 4
- Pages
- Article #S2R32–Article #S2R32
- Publication date
- 10 July 2026
- Language
- EN