Jean-Luc Baril

activity

20152026

most citedRight-jumps and pattern avoiding permutations

4 citations · 9 across the 34 of their papers we have counts for

collaborators

40 papers

math.CO2026

Fibonacci Polyominoes: Refined Enumeration and Dyck-Path Bijections

Jean-Luc Baril, José L. Ramírez, Samuel Ramírez

We study Fibonacci polyominoes, a class of column-convex polyominoes whose lower boundary is a staircase path made of unit horizontal and vertical steps. We derive generating funct…

cs.DM2026

Fibonacci and Catalan Numbers Meet in Staircase Polyominoes

Jean-Luc Baril, José Luis Ramírez, Samuel Ramírez +1

We study Fibonacci (staircase) polyominoes, a class of column-convex polyominoes whose lower boundary is a staircase with unit vertical steps. We derive multivariate generating fun…

math.CO2026

Enumerations and Bijections for Stanley Polyominoes

Jean-Luc Baril, Aubrey Blecher, José Luis ramírez

Stanley polyominoes are a subclass of parallelogram polyominoes in which each row begins strictly to the right of the beginning of the previous row and ends strictly to the right o…

math.CO2026

Black Cell Capacity in Catalan polyominoes

Jean-Luc Baril, Sela Fried, Nathanaël Hassler +1

A Catalan word is a sequence $w_{1} w_{2} \dots w_{n}$ of nonnegative integers such that $w_{1} = 0$ and $w_{i} \leq w_{i - 1} + 1$ for $2 \leq i \leq n$ . Given a Catalan word, we construct a column…

math.CO2025

Enumeration of paths in a hexagonal circle packing

Jean-Luc Baril, José Luis Ramí rez

We investigate paths in the hexagonal circle packing and enumerate them with respect to width, height, number of steps, area, and kissing number. Functional equations and the kerne…

math.CO2025

Enumeration in the lattice of $q$ -decreasing words

Jean-Luc Baril, Nathanaël Hassler, Sergey Kirgizov

We prove that the poset of $q$ -decreasing words equipped with the componentwise order forms a lattice. We enumerate the join-irreducible elements for arbitrary $q > 0$ , and for any p…

math.CO2025

Enumeration on polyominoes determined by Catalan words avoiding $(\geq, \geq)$

M. Ahmia, J. -L. Baril, B. Rezig

A Catalan word of length $n$ that avoids the pattern $(\geq, \geq)$ is a sequence $w = w_{1} \dots w_{n}$ with $w_{1} = 0$ and $0 \leq w_{i} \leq w_{i - 1} + 1$ for all $i$ , while ensuring that no s…

math.CO2024

Intervals in a family of Fibonacci lattices

Jean-Luc Baril, Nathanaël Hassler

We focus on a family of subsets $(\F^p_n)_{p\geq 2}$ of Dyck paths of semilength $n$ that avoid the patterns $D U U$ and $D^{p + 1}$ , which are enumerated by the generalized Fibonacci…

math.CO2024

Some distributions in increasing and flattened permutations

Jean-Luc Baril, José L. Ramírez

We examine the distribution and popularity of different parameters (such as the number of descents, runs, valleys, peaks, right-to-left minima, and more) on the sets of increasing…

math.CO2024

The ascent lattice on Dyck paths

Jean-Luc Baril, Mireille Bousquet-Mélou, Sergey Kirgizov +1

In the Stanley lattice defined on Dyck paths of size $n$ , cover relations are obtained by replacing a valley $D U$ by a peak $U D$ . We investigate a greedy version of this lattice, f…

math.CO2024

Flattened Catalan Words

Jean-Luc Baril, Pamela E. Harris, José L. Ramírez

In this work, we define flattened Catalan words as Catalan words whose runs of weak ascents have leading terms that appear in weakly increasing order. We provide generating functio…

math.CO2024

Enumerating runs, valleys, and peaks in Catalan words

Jean-Luc Baril, Pamela E. Harris, Kimberly J. Harry +2

We provide generating functions, formulas, and asymptotic expressions for the number of Catalan words based on the number of runs of ascents (descents), runs of weak ascents (desce…

math.CO2024

Grand zigzag knight's paths

Jean-Luc Baril, Nathanaël Hassler, Sergey Kirgizov +1

We study the enumeration of different classes of grand knight's paths in the plane. In particular, we focus on the subsets of zigzag knight's paths that are subject to constraints.…

math.CO2024

The Combinatorics of Motzkin Polyominoes

Jean-Luc Baril, Sergey Kirgizov, José L. Ramírez +1

A word $w = w_{1} \dots w_{n}$ over the set of positive integers is a Motzkin word whenever $w_{1} = 1$ , $1 \leq w_{k} \leq w_{k - 1} + 1$ , and $w_{k - 1} \neq = w_{k}$ for $k = 2, \dots, n$ . It c…

math.CO2023

A lattice on Dyck paths close to the Tamari lattice

Jean-Luc Baril, Sergey Kirgizov, Mehdi Naima

We introduce a new poset structure on Dyck paths where the covering relation is a particular case of the relation inducing the Tamari lattice. We prove that the transitive closure…

math.CO2023

Descent distribution on Catalan words avoiding ordered pairs of Relations

Jean-Luc Baril, José Luis Ramírez

This work is a continuation of some recent articles presenting enumerative results for Catalan words avoiding one or a pair of consecutive or classical patterns of length $3$ . More…

math.CO2023

Partial Motzkin paths with air pockets of the first kind avoiding peaks, valleys or double rises

Jean-Luc Baril, José Luis Ramírez

Motzkin paths with air pockets (MAP) of the first kind are defined as a generalization of Dyck paths with air pockets. They are lattice paths in $N^{2}$ starting at the orig…

math.CO2022

Two kinds of partial Motzkin paths with air pockets

Jean-Luc Baril, Paul Barry

Motzkin paths with air pockets (MAP) are defined as a generalization of Dyck paths with air pockets by adding some horizontal steps with certain conditions. In this paper, we intro…

math.CO2022

Grand Dyck paths with air pockets

Jean-Luc Baril, Sergey Kirgizov, Rémi Maréchal +1

Grand Dyck paths with air pockets (GDAP) are a generalization of Dyck paths with air pockets by allowing them to go below the $x$ -axis. We present enumerative results on GDAP (or t…

math.CO2022

Knight's paths towards Catalan numbers

Jean-Luc Baril, José Luis Ramirez

We provide enumerating results for partial knight's paths of a given size. We prove algebraically that zigzag knight's paths of a given size ending on the $x$ -axis are enumerated b…

math.CO2022

Enumeration of partial Lukasiewicz paths

Jean-Luc Baril, Helmut Prodinger

Łukasiewicz paths are lattice paths in $N^{2}$ starting at the origin, ending on the $x$ -axis, and consisting of steps in the set ${(1, k), k \geq - 1}$ . We give generating func…

math.CO2022

Dyck paths with catastrophes modulo the positions of a given pattern

Jean-Luc Baril, Sergey Kirgizov, Armen Petrossian

For any pattern $p$ of length at most two, we provide generating functions and asymptotic approximations for the number of $p$ -equivalence classes of Dyck paths with catastrophes,…

cs.DM2022★ 1 cited

Enumeration of Dyck paths with air pockets

Jean-Luc Baril, Sergey Kirgizov, Rémi Maréchal +1

We introduce and study the new combinatorial class of Dyck paths with air pockets. We exhibit a bijection with the peakless Motzkin paths which transports several pattern statistic…

math.CO2021

Lattice paths with a first return decomposition constrained by the maximal height of a pattern

Jean-Luc Baril, Sergey Kirgizov

We consider the system of equations $A_{k} (x) = p (x) A_{k - 1} (x) (q (x) + \sum_{i = 0}^{k} A_{i} (x))$ for $k \geq r + 1$ where $A_{i} (x)$ , $0 \leq i \leq r$ , are some given functions and show how to obt…

Fibonacci Polyominoes: Refined Enumeration and Dyck-Path Bijections

Fibonacci and Catalan Numbers Meet in Staircase Polyominoes

Enumerations and Bijections for Stanley Polyominoes

Black Cell Capacity in Catalan polyominoes

Enumeration of paths in a hexagonal circle packing

Enumeration in the lattice of q-decreasing words

Enumeration on polyominoes determined by Catalan words avoiding (≥,≥)

Intervals in a family of Fibonacci lattices

Some distributions in increasing and flattened permutations

The ascent lattice on Dyck paths

Flattened Catalan Words

Enumerating runs, valleys, and peaks in Catalan words

Grand zigzag knight's paths

The Combinatorics of Motzkin Polyominoes

A lattice on Dyck paths close to the Tamari lattice

Descent distribution on Catalan words avoiding ordered pairs of Relations

Partial Motzkin paths with air pockets of the first kind avoiding peaks, valleys or double rises

Two kinds of partial Motzkin paths with air pockets

Grand Dyck paths with air pockets

Knight's paths towards Catalan numbers

Enumeration of partial Lukasiewicz paths

Dyck paths with catastrophes modulo the positions of a given pattern

Enumeration of Dyck paths with air pockets

Lattice paths with a first return decomposition constrained by the maximal height of a pattern

Enumeration in the lattice of $q$ -decreasing words

Enumeration on polyominoes determined by Catalan words avoiding $(\geq, \geq)$