# On Characters of a Class of P-polynomial table algebras and applications

## TL;DR

This paper investigates the characters of a specific class of P-polynomial table algebras, develops new methods involving tridiagonal matrices and Z-transform, and applies findings to association schemes.

## Contribution

It introduces novel techniques for analyzing characters of P-polynomial table algebras and computes eigenvalues of key tridiagonal matrices relevant to the structure.

## Key findings

- Derived methods using tridiagonal matrices and Z-transform
- Calculated eigenvalues of a special tridiagonal matrix
- Applied results to association schemes

## Abstract

In this paper, we study the characters of homogeneous monotonic P-polynomial table algebras with finite dimension d>=5. We then apply them to association schemes. To this end, we develop some methods using tridiagonal matrices and Z-transform. Moreover, we calculate the eigenvalues of a special tridiagonal matrix which is found through the first intersection matrix of P-polynomial table algebras.