## Fringe Analysis of Plane Trees Related to Cutting and Pruning

This is joint work with Clemens Heuberger, Sara Kropf, and Helmut Prodinger. The paper can be found on the corresponding arXiv-page arXiv:1704.01095.

The following files contain the computational aspects (like asymptotic expansions) of our results:

- treereductions.ipynb
- old_paths.ipynb
- factorial_moments_leaves.ipynb
- factorial_moments_old_paths.ipynb

In order to run those files, you will need to put the following two files containing utility code into the same directory as the files above:

If you are not familiar with SageMath-files, then here are some instructions explaining how you can run them.

## Using the SageMath files

This is a short guide on how to use and/or process the ancillary files of this paper. These files contain the computational results of our paper, as well as some numerical comparisons. The computations are carried out with the free open-source mathematics software system SageMath. In order to run our files, you need to access SageMath in some way. In general, there are two viable options for this.

### Option 1: Installing SageMath locally on your computer

In order to install SageMath locally, please follow the instructions in the SageMath installation guide.

As soon as you have a running version of SageMath, you can start a local notebook server with the command

1 |
sage -n jupyter |

Then, a tab in your browser shoud open where you can navigate and select the `ipynb`

-file in order to view its content and to execute our computations.

### Option 2: Using SageMathCloud (online)

Navigate to https://cloud.sagemath.com/ and register for a free account or sign in if you already have an account. Then, create a new project (or open an existing one) and click the “New”-Button in order to upload the `ipynb`

-file to the cloud. Afterwards, it can be found among the files of your project, and you can open it as usual.

Note that you might need to adapt the kernel to a more recent SageMath-version (`sage-7.4`

or above should be okay).