Counting symmetric unimodular triangulations
Kamillo Ferry, Michael Joswig, J\"org Rambau
TL;DR
This paper investigates symmetric unimodular triangulations of dilated standard triangles, providing bounds and enumerations for small cases, motivated by applications to T-curves.
Contribution
It offers new bounds and complete enumerations for symmetric unimodular triangulations, advancing understanding in geometric combinatorics.
Findings
Established lower and upper bounds for symmetric unimodular triangulations.
Provided full enumerations for small cases.
Connected triangulation properties to T-curve applications.
Abstract
The objects of study are triangulations of the dilated standard triangle in the plane. Motivated by work on T-curves (Geiselmann et al., 2026), the focus lies on unimodular triangulations with a fixed symmetry axis. Lower and upper bounds are given, in combination with full enumerations of a few small cases.
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