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 language | English |
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Article number | 21.2.8 |
Pages (from-to) | 1-19 |
Number of pages | 19 |
Journal | Journal of Integer Sequences |
Volume | 24 |
Issue number | 2 |
State | Published - 2021 |
Keywords
- Bijection
- Corridor path
- Dyck prefix
- Grand Dyck path
- Lattice path
- Path enumeration