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The enumeration of inversion sequences avoiding the patterns 201 and 210 (2310.19632v3)

Published 30 Oct 2023 in math.CO

Abstract: We derive the algebraic generating function for inversion sequences avoiding the patterns $201$ and $210$ by describing a set of succession rules, converting them to a system of generating function equations with one catalytic variable, and then solving the system with kernel method techniques.

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References (25)
  1. Consecutive patterns in inversion sequences. Discrete Math. Theor. Comput. Sci., 21(2):Paper No. 6, 22, 2019.
  2. Consecutive patterns in inversion sequences II: Avoiding patterns of relations. J. Integer Seq., 22(7):Art. 19.7.5, 37, 2019.
  3. Semi-Baxter and strong-Baxter: two relatives of the Baxter sequence. SIAM J. Discrete Math., 32(4):2795–2819, 2018.
  4. Polynomial equations with one catalytic variable, algebraic series and map enumeration. J. Combin. Theory Ser. B, 96(5):623–672, 2006.
  5. Two examples of unbalanced Wilf-equivalence. J. Comb., 6(1-2):55–67, 2015.
  6. Enumeration of inversion sequences avoiding triples of relations. Discrete Appl. Math., 260:86–97, 2019.
  7. Inversion sequences avoiding a triple of patterns of 3 letters. Electron. J. Combin., 30(3):Paper No. 3.19, 39, 2023.
  8. A bijection for length-5 patterns in permutations. J. Combin. Theory Ser. A, 202:Paper No. 105815, 34, 2024.
  9. Patterns in inversion sequences I. Discrete Math. Theor. Comput. Sci., vol. 18 no. 2, Permutation Patterns 2015, March 2016.
  10. Andrew R. Conway. The design of efficient dynamic programming and transfer matrix enumeration algorithms. J. Phys. A, 50(35):353001, 28, 2017.
  11. An algorithmic approach based on generating trees for enumerating pattern-avoiding inversion sequences. J. Symbolic Comput., 120:Paper No. 102231, 18, 2024.
  12. Donald E. Knuth. The Art of Computer Programming. Vol. 1: Fundamental Algorithms. Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont, 1969.
  13. Donald E. Knuth. The Art of Computer Programming. Vol. 3: Sorting and Searching. Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont, 1973.
  14. Quadrant marked mesh patterns. J. Integer Seq., 15(4):Article 12.4.7, 29, 2012.
  15. Zhicong Lin. Personal communication, 2023.
  16. Toufik Mansour. Five classes of pattern avoiding inversion sequences under one roof: generating trees. J. Difference Equ. Appl., 29(7):748–762, 2023.
  17. Pattern avoidance in inversion sequences. Pure Math. Appl. (PU.M.A.), 25(2):157–176, 2015.
  18. Patterns in inversion sequences II: inversion sequences avoiding triples of relations. J. Integer Seq., 21(2):Art. 18.2.2, 44, 2018.
  19. Jay Pantone. Succession rules for inversion classes avoiding one pattern of length three. (forthcoming).
  20. Neil J. A. Sloane. The Online Encyclopedia of Integer Sequences. https://oeis.org.
  21. Benjamin Testart. Inversion sequences avoiding the pattern 010. https://arxiv.org/abs/2212.07222v2, 2022.
  22. Benjamin Testart. Inversion sequences avoiding pairs of patterns. https://pp2023.permutationpatterns.com/p/testart.pdf, 2023. Permutation Patterns 2023.
  23. Vincent Vatter. Finitely labeled generating trees and restricted permutations. J. Symbolic Comput., 41(5):559–572, 2006.
  24. Gökhan Yıldırım. Personal communication, 2023.
  25. Inversion sequences avoiding pairs of patterns. Discrete Math. Theor. Comput. Sci., 22(1):Paper No. 23, 35, [2020–2021].
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