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universal-partial-tori

Code and data supporting the paper Universal Partial Tori

https://github.com/wcarey-gmu/universal-partial-tori

Science Score: 54.0%

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    CITATION.cff file
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    Links to: arxiv.org
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    Low similarity (6.6%) to scientific vocabulary
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Repository

Code and data supporting the paper Universal Partial Tori

Basic Info
  • Host: GitHub
  • Owner: wcarey-gmu
  • License: mit
  • Language: Python
  • Default Branch: main
  • Size: 30.3 KB
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  • Stars: 0
  • Watchers: 1
  • Forks: 0
  • Open Issues: 0
  • Releases: 0
Created about 1 year ago · Last pushed about 1 year ago
Metadata Files
Readme License Citation

README.md

universal-partial-tori

Code and data supporting the paper Universal Partial Tori. A De Bruijn cycle is a cyclic sequence in which every word of length n over an alphabet appears exactly once. De Bruijn tori are a two-dimensional analogue. Motivated by recent progress on universal partial cycles and words, which shorten De Bruijn cycles using a wildcard character, we introduce universal partial tori and matrices. We find them computationally and construct infinitely many of them using one-dimensional variants of universal cycles, including a new variant called a universal partial family.

Data

This folder contains examples of upmatrices and uptori identified or constructed by the code in this repository. Each file contains a collection of objects for a particular combination of alphabet and subarray dimensions and is named accordingly. The general scheme for the name of the files is object[s]-alphabet-rows-columns.txt. For example, upmatrix-2-3-4.txt would contain a single upmatrix for the binary alphabet whose subarrays have three rows and four columns. Likewise, upmatrices-2-2-2.txt would contain more than one upmatrix for the binary alphabet whose subarrays have two rows and two columns. Note that the objects in a particular file may have different dimensions (e.g. upmatrices-2-2-2.txt contains some upmatrices with 3 rows and 5 columns and some upmatrices with 4 rows and 4 columns).

Within the files, each individual obejct is formatted with a newline after each row and two newlines between objects. The w character represents the "wildcard", which we usually represent as $\diam$ in our paper.

Code

This folder contains libraries for manipulating cyclic combinatorial objects in one and two dimensions. The /apps folder contains programs used to generate examples in the paper.

Owner

  • Login: wcarey-gmu
  • Kind: user

Citation (CITATION.cff) 

# This CITATION.cff file was generated with cffinit.
# Visit https://bit.ly/cffinit to generate yours today!

cff-version: 1.2.0
title: Universal Partial Tori
message: >-
  If you use this software, please cite it using the
  metadata from this file.
type: software
authors:
  - given-names: William
    name-particle: D
    family-names: Carey
    email: wcarey1@gmu.edu
    affiliation: George Mason University
  - given-names: Matthew
    family-names: Kearney
    email: mkearne@gmu.edu
    affiliation: George Mason University
  - given-names: Rachel
    family-names: Kirsch
    email: rkirsch4@gmu.edu
    affiliation: George Mason University
  - given-names: Stefan
    family-names: Popescu
    email: spopesc@gmu.edu
    affiliation: George Mason University
identifiers:
  - type: url
    value: 'https://arxiv.org/abs/2409.12417'
    description: ArXiv URL of the paper that prompted this development
abstract: >-
  A De Bruijn cycle is a cyclic sequence in which every word
  of length $n$ over an alphabet $\A$ appears exactly once.
  De Bruijn tori are a two-dimensional analogue. Motivated
  by recent progress on universal partial cycles and words,
  which shorten De Bruijn cycles using a wildcard character,
  we introduce universal partial tori and matrices. We find
  them computationally and construct infinitely many of them
  using one-dimensional variants of universal cycles,
  including a new variant called a universal partial family.
keywords:
  - universal partial torus
  - universal word
license: MIT
url: "https://github.com/wcarey-gmu/universal-partial-tori"

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