13 citations · 31 across the 22 of their papers we have counts for
20 papers · 1 filter
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…
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 .…
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{…
Strings from linear recurrences and permutations: a Gray code
Elena Barcucci, Antonio Bernini, Renzo Pinzani
Each positive increasing integer sequence can serve as a numeration system to represent each non-negative integer by means of suitable coefficient strings. We a…
A Construction for Variable Dimension Strong Non-Overlapping Matrices
Elena Barcucci, Antonio Bernini, Stefano Bilotta +1
We propose a method for the construction of sets of variable dimension strong non-overlapping matrices basing on any strong non-overlapping set of strings.
On the generating functions of pattern-avoiding Motzkin paths
Christian Bean, Antonio Bernini, Matteo Cervetti +1
Using a recursive approach, we show that the generating function for sets of Motzkin paths avoiding a single (not necessarily consecutive) pattern is rational over and the Cata…