An algorithmic approach based on generating trees for enumerating pattern-avoiding inversion sequences

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buir.contributor.authorYıldırım, Gökhan
buir.contributor.orcidYıldırım, Gökhan|0000-0003-4399-7843
dc.citation.epage102231-18en_US
dc.citation.issueNumberJanuary–February 2024
dc.citation.spage102231-1
dc.citation.volumeNumberVolume 120
dc.contributor.authorKotsireas, I.
dc.contributor.authorMansour, T.
dc.contributor.authorYıldırım, Gökhan
dc.date.accessioned2024-03-12T14:59:32Z
dc.date.available2024-03-12T14:59:32Z
dc.date.issued2023-05-18
dc.departmentDepartment of Mathematics
dc.description.abstractWe introduce an algorithmic approach based on a generating tree method for enumerating the inversion sequences with various pattern-avoidance restrictions. For a given set of patterns, we propose an algorithm that outputs either an accurate description of the succession rules of the corresponding generating tree or an ansatz. By using this approach, we determine the generating trees for the pattern classes In(000, 021), In(100, 021), In(110, 021), In(102, 021), In(100, 012), In(011, 201), In(011, 210) and In(120, 210). Then we use the kernel method, obtain generating functions of each class, and find enumerating formulas. Lin and Yan studied the classification of the Wilf-equivalences for inversion sequences avoiding pairs of length-three patterns and showed that there are 48 Wilf classes among 78 pairs. In this paper, we solve six open cases for such pattern classes. Moreover, we extend the algorithm to restricted growth sequences and apply it to several classes. In particular, we present explicit formulas for the generating functions of the restricted growth sequences that avoid either {12313, 12323}, {12313, 12323, 12333}, or {123 ··· 1}.
dc.identifier.doi10.1016/j.jsc.2023.102231
dc.identifier.eissn1095-855X
dc.identifier.issn0747-7171
dc.identifier.urihttps://hdl.handle.net/11693/114629
dc.language.isoen_US
dc.publisherAcademic Press Ltd- Elsevier Science Ltd
dc.relation.isversionofhttps://dx.doi.org/10.1016/j.jsc.2023.102231
dc.rightsCC BY 4.0 DEED (Attribution 4.0 International)
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.source.titleJournal of Symbolic Computation
dc.subjectPattern-avoiding inversion sequences
dc.subjectGenerating functions
dc.subjectGenerating trees
dc.subjectKernel method
dc.subjectCatalan numbers
dc.subjectMotzkin numbers
dc.titleAn algorithmic approach based on generating trees for enumerating pattern-avoiding inversion sequences
dc.typeArticle
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