Satisfying states of triangulations of a convex n-gon

TL;DR

This paper counts the satisfying states of triangulations of convex polygons using transfer matrix methods, providing an exact formula for strips and establishing an exponential lower bound for general cases.

Contribution

It introduces a transfer matrix approach to count satisfying states and derives an exact formula for strips, along with an exponential lower bound for general triangulations.

Findings

Exact formula for satisfying states of a strip of triangles

Exponential lower bound for the number of satisfying states

Application of transfer matrix method to triangulation enumeration

Abstract

In this work we count the number of satisfying states of triangulations of a convex n-gon using the transfer matrix method. We show an exponential (in n) lower bound. We also give the exact formula for the number of satisfying states of a strip of triangles.