k-Naples parking functions are counted recursively, characterized for k=1 by a map to classical parking functions, and bijected to signature Dyck paths.
Konheim and Benjamin Weiss, An occupancy discipline and applications , Siam Journal on Applied Mathematics - SIAMAM 14 (196611).↑1, 2, 6
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A Generalization of Parking Functions Allowing Backward Movement
k-Naples parking functions are counted recursively, characterized for k=1 by a map to classical parking functions, and bijected to signature Dyck paths.