We consider Dyck paths having height at most two with some constraints on the number of consecutive valleys at height one which must be followed by a suitable number of valleys at height zero. We prove that they are enumerated by so-called Q-bonacci numbers (recently introduced by Kirgizov) which generalize the classical q-bonacci numbers in the case where q is a positive rational.
Dyck Paths Enumerated by the Q-bonacci Numbers / Barcucci E.; Bernini A.; Bilotta S.; Pinzani R.. - In: ELECTRONIC PROCEEDINGS IN THEORETICAL COMPUTER SCIENCE. - ISSN 2075-2180. - ELETTRONICO. - 403:(2024), pp. 49-53. (Intervento presentato al convegno 13th Conference on Random Generation of Combinatorial Structures. Polyominoes and Tilings, GASCom 2024 tenutosi a fra nel 2024) [10.4204/EPTCS.403.13].
Dyck Paths Enumerated by the Q-bonacci Numbers
Barcucci E.;Bernini A.
;Bilotta S.;Pinzani R.
2024
Abstract
We consider Dyck paths having height at most two with some constraints on the number of consecutive valleys at height one which must be followed by a suitable number of valleys at height zero. We prove that they are enumerated by so-called Q-bonacci numbers (recently introduced by Kirgizov) which generalize the classical q-bonacci numbers in the case where q is a positive rational.
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