A spectral equivalent condition of the $P$-polynomial property for association schemes

TL;DR

This paper establishes a spectral condition that characterizes when a symmetric association scheme has the $P$-polynomial property, providing a new perspective on the algebraic structure of these schemes.

Contribution

It introduces a spectral criterion that is equivalent to the $P$-polynomial property in symmetric association schemes, advancing theoretical understanding.

Findings

Spectral condition equivalent to $P$-polynomial property

New characterization of symmetric association schemes

Enhanced algebraic understanding of association schemes

Abstract

We give an equivalent condition of the $P$-polynomial property of symmetric association schemes.