Combinatorial generation via permutation languages. I. Fundamentals

@article{Hartung2020CombinatorialGV,
  title={Combinatorial generation via permutation languages. I. Fundamentals},
  author={Elizabeth J. Hartung and Hung Phuc Hoang and Torsten M{\"u}tze and Aaron Williams},
  journal={ArXiv},
  year={2020},
  volume={abs/1906.06069}
}
In this work we present a general and versatile algorithmic framework for exhaustively generating a large variety of different combinatorial objects, based on encoding them as permutations. This approach provides a unified view on many known results and allows us to prove many new ones. In particular, we obtain four classical Gray codes for permutations, bitstrings, binary trees and set partitions as special cases. We present two distinct applications for our new framework: The first main… 
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A general and versatile algorithmic framework for exhaustively generating a large variety of different combinatorial objects, based on encoding them as permutations, which provides a unified view on many known results and allows us to prove many new ones.
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