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math.CO2022★ 2 cited
Enumeration of Generalized Dyck Paths Based on the Height of Down-Steps Modulo
Clemens Heuberger, Sarah J. Selkirk, Stephan Wagner
For fixed non-negative integers , , and , with , a -Dyck path of length is a lattice path that starts at , ends at , stays weakly…
math.CO2022
A Note on the Relation between Recognisable Series and Regular Sequences, and their Minimal Linear Representations
Clemens Heuberger, Daniel Krenn, Gabriel F. Lipnik
In this note, we precisely elaborate the connection between recognisable series (in the sense of Berstel and Reutenauer) and -regular sequences (in the sense of Allouche and Sha…