13 citations · 34 across the 27 of their papers we have counts for
19 papers · 1 filter
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.
Variable dimension non-overlapping matrices
Elena Barcucci, Antonio Bernini, Renzo Pinzani
Since some years, non-overlapping sets of strings (also called cross-bifix-free sets) have had an increasing interest in the frame of the researches about Theory of Codes. Recently…
Non-overlapping Dyck matrices
Elena Barcucci, Antonio Bernini, Stefano Bilotta +2
We define a set of binary matrices where any two of them can not be placed one on the other in a way such that the corresponding entries coincide. The rows of the matrices are obta…
Cross-bifix-free sets via Motzkin paths generation
Elena Barcucci, Stefano Bilotta, Elisa Pergola +2
Cross-bifix-free sets are sets of words such that no prefix of any word is a sufix of any other word. In this paper, we introduce a general constructive method for the sets of cros…
Gray code orders for -ary words avoiding a given factor
A. Bernini, S. Bilotta, R. Pinzani +2
Based on BRGC inspired order relations we give Gray codes and a generating algorithm for -ary words avoiding a prescribed factor. These generalize an early 2001 result and a ver…
A trace partitioned Gray code for q-ary generalized Fibonacci strings
Antonio Bernini, Stefano Bilotta, Renzo Pinzani +1
We provide a trace partitioned Gray code for the set of q-ary strings avoiding a pattern constituted by k consecutive equal symbols. The definition of this Gray code is based on tw…
The Dyck pattern poset
Antonio Bernini, Luca Ferrari, Renzo Pinzani +1
We introduce the notion of pattern in the context of lattice paths, and investigate it in the specific case of Dyck paths. Similarly to the case of permutations, the pattern-contai…
Catalan lattices on series parallel interval orders
Filippo Disanto, Luca Ferrari, Renzo Pinzani +1
Using the notion of series parallel interval order, we propose a unified setting to describe Dyck lattices and Tamari lattices (two well known lattice structures on Catalan objects…
Catalan numbers and relations
Filippo Disanto, Luca Ferrari, Renzo Pinzani +1
We define the notion of a Catalan pair (which is a pair of binary relations (S,R) satisfying certain axioms) with the aim of giving a common language to most of the combinatorial i…
Six bijections between deco polyominoes and permutations
Emeric Deutsch, Elisa Pergola, Renzo Pinzani
In this paper we establish six bijections between a particular class of polyominoes, called deco polyominoes, enumerated according to their directed height by n!, and permutations.…
Mixed succession rules: the commutative case
Silvia Bacchelli, Luca Ferrari, Renzo Pinzani +1
We begin a systematic study of the enumerative combinatorics of mixed succession rules, which are succession rules such that, in the associated generating tree, the nodes are allow…
Enumeration of some classes of words avoiding two generalized patterns of length three
Antonio Bernini, Luca Ferrari, Renzo Pinzani
The method we have applied in "A. Bernini, L. Ferrari, R. Pinzani, Enumerating permutations avoiding three Babson-Steingrimsson patterns, Ann. Comb. 9 (2005), 137--162" to count pa…
A general exhaustive generation algorithm for Gray structures
Antonio Bernini, Elisabetta Grazzini, Elisa Pergola +1
Starting from a succession rule for Catalan numbers, we define a procedure encoding and listing the objects enumerated by these numbers such that two consecutive codes of the list…
A closed formula for the number of convex permutominoes
Filippo Disanto, Andrea Frosini, Renzo Pinzani +1
In this paper we determine a closed formula for the number of convex permutominoes of size n. We reach this goal by providing a recursive generation of all convex permutominoes of…
Catalan-like numbers and succession rules
Luca Ferrari, Renzo Pinzani
The ECO method and the theory of Catalan-like numbers introduced by Aigner seems two completely unrelated combinatorial settings. In this work we try to establish a bridge between…
Lattices of lattice paths
Luca Ferrari, Renzo Pinzani
We consider posets of lattice paths (endowed with a natural order) and begin the study of such structures. We give an algebraic condition to recognize which ones of these posets ar…