3 papers
math.CO2026
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…
cs.DS2026
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…
cs.DM2026
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…