Growth Series of Cyclotomic Lattices and Cyclotomic Polytopes

Serkan Hosten, SFSU

Cyclotomic lattices are abelian groups generated by the set M(m) of a primitive m-th root of unity and its powers. The growth series of this lattice is the generating function for the word length of its elements with respect to M(m). We settle a few conjectures about the numerator polynomial of the growth series. In particular, we show that the coefficients of this polynomial are nonnegative, unimodal, and palindromic when m is divisible by at most two odd primes. These results are obtained by studying the cyclotomic polytope C_m. The talk is based on joint work with Matthias Beck.