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 |
|---|---|
| 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