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Growth Series of Cyclotomic Lattices and Cyclotomic Polytopes

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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.