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Constrained Underdiagonal Paths and Pattern Avoiding Permutations

Author

Listed:
  • Andrea Frosini

    (Department of Mathematics and Informatics, University of Firenze, 50141 Florence, Italy)

  • Veronica Guerrini

    (Department of Informatics, University of Pisa, 56127 Pisa, Italy)

  • Simone Rinaldi

    (Department of Information Engineering and Mathematics, University of Siena, 53100 Siena, Italy)

Abstract

Moving from a simple bijection P between permutations S n of length n and underdiagonal paths of size n , The we study and enumerate families of underdiagonal paths which are defined by restricting the bijection P to subclasses of S n avoiding some vincular patterns. In particular, we will consider patterns of lengths 3 and 4, and, when it is possible, we will provide a characterization of the underdiagonal paths related to them in terms of geometrical constraints, or equivalently, the avoidance of some factors. Finally, we will provide a recursive growth of these families by means of generating trees and then their enumerative sequence.

Suggested Citation

  • Andrea Frosini & Veronica Guerrini & Simone Rinaldi, 2025. "Constrained Underdiagonal Paths and Pattern Avoiding Permutations," Mathematics, MDPI, vol. 13(3), pages 1-19, February.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:3:p:517-:d:1583304
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