Abstract
ECO-method and its corresponding succession rules allow to recursively define and construct combinatorial objects. The induced generating trees can be coded by corresponding pattern avoiding permutations. We refine succession rules by using succession functions in case when avoided patterns are regular or c-regular. Although regular patterns are hard to be recognized in general, we give a characterization for its right-justified property which is a prerequisite in the definition of the regular pattern. Based on this characterization, we show the (c-)regularity for various classes of permutations avoiding sets of patterns with variable lengths. Last, the technique of succession functions permits to construct general recursive generating models for classes of (c-) regular pattern avoiding permutations, which are constant amortized time for all classes mentioned in the paper.
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Acknowledgment
This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 102.01-2016.05. The second author is partially funded by the PSSG No.6.
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Do, P.T., Tran, T.T.H., Vajnovszki, V. (2017). Right-Justified Characterization for Generating Regular Pattern Avoiding Permutations. In: Blömer, J., Kotsireas, I., Kutsia, T., Simos, D. (eds) Mathematical Aspects of Computer and Information Sciences. MACIS 2017. Lecture Notes in Computer Science(), vol 10693. Springer, Cham. https://doi.org/10.1007/978-3-319-72453-9_25
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DOI: https://doi.org/10.1007/978-3-319-72453-9_25
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