Counting components of an integral lamination

TL;DR

This paper introduces an efficient algorithm to determine the number of components in an integral lamination on an n-punctured disk using Dynnikov coordinates, optimizing computational complexity.

Contribution

The paper presents a novel algorithm that computes lamination components from Dynnikov coordinates with improved efficiency over previous methods.

Findings

Algorithm requires O(n^2 M) operations, where M is sum of absolute Dynnikov coordinates.

Efficient computation of lamination components from Dynnikov coordinates.

Applicable to n-punctured disks in topological studies.

Abstract

We present an efficient algorithm for calculating the number of components of an integral lamination on an $n$-punctured disk, given its Dynnikov coordinates. The algorithm requires $O(n^2M)$ arithmetic operations, where $M$ is the sum of the absolute values of the Dynnikov coordinates.