4 papers
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…
A generating tree with a single label for permutations avoiding the vincular pattern 1-32-4
Matteo Cervetti
In this paper we continue the study of permutations avoiding the vincular pattern by constructing a generating tree with a single label for these permutations. This constr…
Pattern avoidance in the matching pattern poset
Matteo Cervetti, Luca Ferrari
A matching of the set is a partition of into blocks with two elements, i.e. a graph on such that every vertex has degree one. Given two mat…
Enumerative combinatorics of intervals in the Dyck pattern poset
Antonio Bernini, Matteo Cervetti, Luca Ferrari +1
We initiate the study of the enumerative combinatorics of the intervals in the Dyck pattern poset. More specifically, we find some closed formulas to express the size of some speci…