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cayleyR: Cayley Graph Analysis for Permutation Puzzles

Analyzes Cayley graphs of permutation puzzles. Any puzzle whose moves permute a fixed set of positions can be declared as a permutation group, and the same tools then work on it: cycle detection, state space exploration and path search. Two puzzles are built in: TopSpin and Rubik's cubes of any size. The 3x3x3 is solved by four human methods and by a two-phase search after Herbert Kociemba; the 4x4x4 is solved by reduction. The Iterative Cycle Intersection (ICI) method is described in Yuri Baramykov (2026) <doi:10.48550/arXiv.2607.13219>.

Version: 0.3.0
Imports: Rcpp, utils
LinkingTo: Rcpp
Suggests: testthat (≥ 3.0.0), ggmlR, parallel, data.table, jsonlite, knitr, rmarkdown
Published: 2026-10-19
DOI: 10.32614/CRAN.package.cayleyR
Author: Yuri Baramykov ORCID iD [aut, cre], Lucas Garron [ctb, cph] (twips search machinery in src/kociemba_core.h, src/kociemba4.h), cubing.js authors [cph] (twips, https://github.com/cubing/twips)
Maintainer: Yuri Baramykov <lbsbmsu at mail.ru>
BugReports: https://github.com/Zabis13/cayleyR/issues
License: MIT + file LICENSE
URL: https://github.com/Zabis13/cayleyR, https://arxiv.org/abs/2607.13219
NeedsCompilation: yes
Materials: README, NEWS
CRAN checks: cayleyR results

Documentation:

Reference manual: cayleyR.html , cayleyR.pdf
Vignettes: The 4x4x4 Cube (source, R code)
Function Reference (source)
Solving Top Spin by Hand (source)
Landmark States and the Solid They Span (source, R code)
Neural Solvers (source, R code)
Permutation Groups (source, R code)
The Rubik's Cube (source, R code)

Downloads:

Package source: cayleyR_0.3.0.tar.gz
Windows binaries: r-devel: cayleyR_0.3.0.zip, r-release: cayleyR_0.3.0.zip, r-oldrel: cayleyR_0.3.0.zip
macOS binaries: r-release (arm64): cayleyR_0.3.0.tgz, r-oldrel (arm64): cayleyR_0.3.0.tgz, r-release (x86_64): cayleyR_0.3.0.tgz, r-oldrel (x86_64): cayleyR_0.3.0.tgz
Old sources: cayleyR archive

Reverse dependencies:

Reverse suggests: cgvR

Linking:

Please use the canonical form https://CRAN.R-project.org/package=cayleyR to link to this page.

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.