Cyclotomic Polytopes and Growth Series of Cyclotomic Lattices
| dc.creator | Beck, Matthias | |
| dc.creator | Hosten, Serkan | |
| dc.date | 2005-08-08 | |
| dc.date | 2006-02-15 | |
| dc.date.accessioned | 2026-07-07T08:07:07Z | |
| dc.date.available | 2026-07-07T08:07:07Z | |
| dc.description | The coordination sequence of a lattice $Ł$ encodes the word-length function with respect to $M$, a set that generates $Ł$ as a monoid. We investigate the coordination sequence of the cyclotomic lattice $Ł= \Z[ζ_m]$, where $ζ_m$ is a primitive $mþ$ root of unity and where $M$ is the set of all $mþ$ roots of unity. We prove several conjectures by Parker regarding the structure of the rational generating function of the coordination sequence; this structure depends on the prime factorization of $m$. Our methods are based on unimodular triangulations of the $mþ$ cyclotomic polytope, the convex hull of the $m$ roots of unity in $\R^{ϕ(m)}$, with respect to a canonically chosen basis of $Ł$. | |
| dc.description | 15 pages | |
| dc.identifier | https://arxiv.org/abs/math/0508136 | |
| dc.identifier | http://arxiv.org/abs/math/0508136 | |
| dc.identifier | Mathematical Research Letters 13, no. 4 (2006), 607-622 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/130837 | |
| dc.subject | Combinatorics | |
| dc.subject | Commutative Algebra | |
| dc.subject | Number Theory | |
| dc.subject | 52C07, 13D40, 11H06; 14M25, 52B20 | |
| dc.title | Cyclotomic Polytopes and Growth Series of Cyclotomic Lattices | |
| dc.type | text |