This codebook.txt file was generated on 20180729 by Samantha Smith. ------------------- GENERAL INFORMATION ------------------- 1. Title of Dataset: Torsion-Free Vertex-Regular Lattices of I55 2. Author Information Name: Samantha Smith Institution: Oregon State University Address: Oregon State University, C/O Mathematics Department, 1500 SW Jefferson St. Corvallis, OR 97331. Email: smitsama@oregonstate.edu Supervisor's Name: William Bogley Institution: Oregon State University Address: Oregon State University, C/O Mathematics Department, 1500 SW Jefferson St. Corvallis, OR 97331. Email: bill.bogley@oregonstate.edu 3. Dataset Summary This dataset contains the text file I55lattices.txt, a list of the sets of relators for all the torsion-free vertex-regular cocompact lattices of Bourdon's building I_{5,5} which is formatted for use with GAP 4. Each entry in the list in I55lattices.txt is itself a list containing 5 lists of length 5 with entries consisting of digits between 0 and 9. Each digit i represents a generator or inverse generator for the corresponding torsion-free vertex-regular cocompact lattice of I_{5,5} according to the following rule: i represents the generator x_i for i < 5, and i represents the inverse generator x_{i-5}^{-1} for i >= 5. Each 5-digit list represents a relator. For example, the list [ 0, 0, 1, 0, 2 ] represents the relator x_0*x_0*x_1*x_0*x_2. In addition, the repository contains the text file relatorstogroups.txt, which contains a GAP 4 program which will convert the sets of relators in I55lattices.txt into finitely presented groups. Finally, the repository contains the text files MakePTuples.txt, MakeNPTuples.txt, ConstructPLattices.txt, ConstructNPLattices.txt, and ClassifyingLattices.txt containing programs written for execution in GAP 4 by which these sets of relators were constructed and the corresponding groups were classified up to isomorphism. -------------------------- SHARING/ACCESS INFORMATION -------------------------- 1. Licenses/restrictions placed on the data: This project is licensed under the MIT licensed -- see the following link for details: https://github.com/JudeNavarre/Lattices-of-I55/blob/master/LICENSE.md 2. Links to publications that cite or use the data: 3. Links to other publicly accessible locations of the data: The GitHub repository: https://github.com/JudeNavarre/Lattices-of-I55 4. Links/relationships to ancillary data sets: None 5. Was data derived from another source? No 6. Recommended citation for the data: Smith, S. T. (2018). Torsion-Free Vertex-Regular Lattices of I55 [Data set]. Oregon State University. https://doi.org/10.7267/PV63G534Q 7. DOI 10.7267/pv63g534q 8. Citeable URL http://ir.library.oregonstate.edu/concern/datasets/pv63g534q --------------------- DATA & FILE OVERVIEW --------------------- 1. File List A. Filename: MakePTuples.txt Short description: This text document contains a series of short programs formatted for execution in the software GAP 4. These programs can be used to produce the 5-tuples which represent potential relators of positive scaffolded presentations of lattices of I55 and is necessary for the execution of the programs in ConstructPLattices.txt. B. Filename: MakeNPTuples.txt Short description: This text document contains a series of short programs formatted for execution in the software GAP 4. These programs can be used to produce the 5-tuples which represent potential relators of non-positive scaffolded presentations of lattices of I55. C. Filename: goodtuples.txt Short description: This text document is formatted to be read by the softwre GAP 4. It was produced using the programs in MakeNPTuples.txt and is necessary to execute the programs in ClassifyNPLattices.txt. D. Filename: newtuples.txt Short description: This text document is formatted to be read by the softwre GAP 4. It was produced using the programs in MakeNPTuples.txt and is necessary to execute the programs in ClassifyNPLattices.txt as well as ConstructNPLattices.txt. E. Filename: ConstructPLattices.txt. Short description: This text document contains a series of short programs formatted for execution in the software GAP 4. It was used to produce the positively presented scaffolded presentations of lattices in the file I55lattices.txt. The programs require the file MakePTuples.txt in order to run. F. Filename: ConstructNPLattices.txt. Short description: This text document contains a series of short programs formatted for execution in the software GAP 4. It was used to produce the non-positively presented scaffolded presentations of lattices in the file I55lattices.txt. The programs require the file newtuples.txt in order to run. G. Filename: ClassifyLattices.txt. Short description: This text document contains a series of short programs formatted for execution in the software GAP 4. It was classify the lattices in I55lattices.txt up to isomorphism. The programs require the files goodtuples.txt and newtuples.txt in order to run. H. Filename: relatorstogroups.txt. Short description: This text document contains a single short program formatted for execution in the software GAP 4. It can be used to convert the lattices in the file I55lattices.txt into finitely presented groups. The program requires the file I55 lattices in order to run. 2. Relationship between files: The programs in ClassifyLattices.txt require newtuples.txt and goodtuples.txt to run. The programs in ConstructNPLattices.txt require newtuples.txt to run. The programs in ConstructPLattices.txt require MakePLattices.txt to run. The program in relatorstogroups.txt requires I55lattices.txt to run. 3. Additional related data collected that was not included in the current data package: None 4. Are there multiple versions of the dataset? None -------------------------- METHODOLOGICAL INFORMATION -------------------------- 1. Description of methods used for collection/generation of data: The methods for the generation of this data are outlined in the dissertation "Rigidity of Vertex-Regular Actions on Fuchsian Buildings" which is linked to this dataset (Smith, Samantha. "Rigidity of Vertex-Regular Actions on Fuchsian Buildings." PhD Thesis. Oregon State University, 2018). 2. Methods for processing the data: The methods for the processing of this data are outlined in the dissertation "Rigidity of Vertex-Regular Actions on Fuchsian Buildings" which is linked to this dataset (Smith, Samantha. "Rigidity of Vertex-Regular Actions on Fuchsian Buildings." PhD Thesis. Oregon State University, 2018). 3. Instrument- or software-specific information needed to interpret the data: Each file in this dataset is formatted compatibly with the software GAP 4 (The GAP Group, GAP - Groups, Algorithms, and Programming, Version 4.8.10; 2018. (https://www.gap-system.org)). Each five-tuple of digits in the files I55lattices.txt, newtuples.txt, and goodtuples.txt represents a word in the free group on 5 generators. The digit i, 0<=i<=4, represents the generator x_i, and each digit i, 5<=i<=9, represents the inverse generator x_{i-5}^{-1}. Every list in I55lattices.txt represents a set of relators determining a finitely presented group. To convert the lists in I55lattices.txt into the corresponding finitely presented groups, begin by downloading both this file and the file relatorstogroups.txt into your GAP directory. Execute the commands Read("I55lattices.txt"); Read("relatorstogroups.txt"); := RelatorsToGroups(I55lattices); The list of finitely presented groups can now be accessed in GAP using the command ; To reproduce the positively presented scaffolded presentations of the lattices of I55, download the files "MakePtuples.txt", "ConstructPLattices.txt", and "ClassifyLattices.txt" to your GAP directory. Then execute the following GAP commands: Read("MakePTuples.txt"); Read("ConstructPLattices.txt"); Read("ClassifyLattices.txt"); tuples := MakePTuples(); allpositivepresentations := ConstructPLattices(tuples); positivepresentations := permiso(positivepresentations); To reproduce the non-positively presented scaffolded presentations of the lattices of I55, download the files "goodtuples.txt", "newtuples.txt", "ConstructNPLattices.txt", and "ClassifyLattices.txt" to your GAP directory. Then execute the following GAP commands: Read("goodtuples.txt"); Read("newtuples.txt"); Read("ConstructPLattices.txt"); Read("ClassifyLattices.txt"); allnppresentations := ConstructNPLattices(newtuples); nppresentations := permiso(allnppresentations); For information abut how to recreate the files "goodtuples.txt" and "newtuples.txt," please see the comments in the file "MakeNPLattices.txt." The complete list of names and arguments of the programs in the files MakePTuples.txt, MakeNPTuples.txt, ConstructPLattices.txt, ConstructNPLattices.txt, and ClassifyLattices.txt have been explained in comments in the respective files. 4. Describe any quality-assurance procedures performed on the data: The tuples produced by the programs in MakePTuples.txt and MakeNPTuples.txt were checked for accuracy by comparing the number of tuples produced with known combinatorial formulas. The functions in ConstructPLattices, ConstructNPLattices, and ClassifyLattices were tested by restricting their inputs so that the validity of the sample outputs could be verified by hand. The size of the restricted inputs varies by function; however, typically 3 sets of inputs of size 10 were used. 5. People involved with sample collection, processing, analysis and/or submission: Samantha Smith