Hall polynomials for Ãn

Abstract.

The purpose of this short note is to present another direct, combinatorial proof for the existence of Hall polynomials of the cyclic quiver à _n . The main point is the using of ideas, results from [5] to extend the beautiful proof of Zelevinsky in [3] for the existence of classical Hall polynomials over discrete valuation rings with finite residue fields to à _n . There are already two other proofs for Hall polynomials over à _n given in [2] and [4]. However, these proofs are of different nature.