13 citations · 31 across the 22 of their papers we have counts for
27 papers
The mex statistic on combinatorial structures
Antonio Bernini, Stefano Bilotta, Giulio Cerbai +1
We extend the notion of mex, which is central in combinatorial number theory, to an arbitrary combinatorial structure, and we prove a general theorem to determine the generating fu…
Random Generation of -coloured Motzkin Paths
Elena Barcucci, Antonio Bernini, Stefano Bilotta +1
We study k-coloured Motzkin paths, namely Motzkin paths in which horizontal steps can be coloured in k different ways, and investigate their connection with the number of prefixes…
An Identity for Catalan Numbers via Restricted Dyck Paths
Antonio Bernini, Stefano Bilotta, Elisa Pergola
Catalan numbers and their interpretations in terms of Dyck paths are widely used in different topics of applied mathematics and computer science. Here, we consider a general approa…
Rational Dyck paths
Elena Barcucci, Antonio Bernini, Stefano Bilotta +1
Given a positive rational , we consider Dyck paths having height at most two with some constraints on the number of consecutive peaks and consecutive valleys, depending on .…
Dyck Paths Enumerated by the Q-bonacci Numbers
Elena Barcucci, Antonio Bernini, Stefano Bilotta +1
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…
Restricting Dyck Paths and 312-avoiding Permutations
Elena Barcucci, Antonio Bernini, Stefano Bilotta +1
Dyck paths having height at most and without valleys at height are combinatorially interpreted by means of 312-avoding permutations with some restrictions on their \emph{…