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

Ilias Kotsireas, Toufik Mansour, Gökhan Yıldırım

Research output: Contribution to journalArticlepeer-review


We 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⋯ℓ1}.

Original languageEnglish
Article number102231
JournalJournal of Symbolic Computation
StatePublished - 1 Jan 2024

Bibliographical note

Publisher Copyright:
© 2023 Elsevier Ltd


  • Catalan numbers
  • Generating functions
  • Generating trees
  • Kernel method
  • Motzkin numbers
  • Pattern-avoiding inversion sequences

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computational Mathematics


Dive into the research topics of 'An algorithmic approach based on generating trees for enumerating pattern-avoiding inversion sequences'. Together they form a unique fingerprint.

Cite this