Loop-free Gray code algorithm for the e-restricted growth functions
Highlights
► We give a Gray code for the set of e-restricted growth functions. ► We obtain a new Gray code for the set partitions. ► We present a loop-free generating algorithm for our Gray code. ► We give some enumerative results concerning our restricted growth functions.
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Gray codes and lexicographical combinatorial generation for nonnesting and sparse nonnesting set partitions
2015, Theoretical Computer ScienceCitation Excerpt :Such theory of Gray codes has a vast range of applications in several areas such as hardware and software testing, thermodynamic, biology and biochemistry; see [3,48] and the references therein. There exist results for (lexicographical) combinatorial generation of several classes of permutations and set partitions, see e.g. [8,20,22,33,35,39,40,50,54,57,58], but so far there are no direct, explicit efficient algorithms for the lexicographical combinatorial generation of noncrossing and nonnesting partitions. Specifically, all known results up to now for generating (not lexicographically) nonnesting partitions use a generating tree approach which often involves passing through Young tableaux or lattice paths, see [10] and the references therein.
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