Between broadway and the hudson: A bijection of corridor paths

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Abstract

We present a substantial generalization of the equinumeracy of Grand Dyck paths and Dyck-path prefixes, constrained within a band. The number of constrained paths starting at level i and ending in a window of size 2j+2 is equal to the number starting at level j and ending in a window of size 2i + 2 centered around the same point. A new encoding of lattice paths provides a bijective proof.

Original languageEnglish
Article number21.2.8
Pages (from-to)1-19
Number of pages19
JournalJournal of Integer Sequences
Volume24
Issue number2
StatePublished - 2021

Keywords

  • Bijection
  • Corridor path
  • Dyck prefix
  • Grand Dyck path
  • Lattice path
  • Path enumeration

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