Between Broadway and the Hudson: A Bijection of Corridor Paths
Nachum Dershowitz
School of Computer Science
Tel Aviv University
Ramat Aviv
Israel
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.
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(Concerned with sequences
A000007
A000012
A000045
A000244
A001519
A003462
A005021
A007051
A011782
A016116
A024175
A025192
A028495
A030436
A033191
A038754
A052975
A060557
A061551
A080936
A080937
A080938
A087944
A087946
A094789
A094790
A124302
A178381
A211216
A336675
A336678.)
Received January 13 2021; revised versions received January 14 2021; January 27 2021; January 30 2021.
Published in Journal of Integer Sequences,
January 30 2021.
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