On the Simplicial Complexes Associated to the Cyclotomic Polynomial

Abstract

Musiker and Reiner in [9] studied coefficients of cyclotomic polynomial in terms of topology of associated simplicial complexes. They determined homotopy type of associated complexes for all cyclotomic polynomials, except for cyclotomic polynomials whose degree is a product of three prime numbers. Using discrete Morse theory for simplicial complexes we partially answer a question posed by the two authors regarding homotopy type of the associated complexes when degree of the cyclotomic polynomial is a product of three prime numbers.