Kyoto Journal of Mathematics
- Kyoto J. Math.
- Volume 57, Number 4 (2017), 807-828.
We discuss generalizations of some results on lattice polygons to certain piecewise linear loops which may have a self-intersection but have vertices in the lattice . We first prove a formula on the rotation number of a unimodular sequence in . This formula implies the generalized twelve-point theorem of Poonen and Rodriguez-Villegas. We then introduce the notion of lattice multipolygons, which is a generalization of lattice polygons, state the generalized Pick’s formula, and discuss the classification of Ehrhart polynomials of lattice multipolygons and also of several natural subfamilies of lattice multipolygons.
Kyoto J. Math., Volume 57, Number 4 (2017), 807-828.
Received: 28 April 2014
Revised: 1 July 2016
Accepted: 6 July 2016
First available in Project Euclid: 22 June 2017
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Higashitani, Akihiro; Masuda, Mikiya. Lattice multipolygons. Kyoto J. Math. 57 (2017), no. 4, 807--828. doi:10.1215/21562261-2017-0016. https://projecteuclid.org/euclid.kjm/1498096939