Sergey Kirgizov

activity

20162026

most citedBijections from Dyck and Motzkin meanders with catastrophes to pattern avoiding Dyck paths

1 citations · 2 across the 19 of their papers we have counts for

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18 papers · 1 filter

math.CO2026

Brick Wall Excursions: Combinatorial Interpretation of Random Flight Moments

Sergey Kirgizov, Khaydar Nurligareev, Michael Wallner

We study the expected distance of short uniform random walks in arbitrary dimensions with unit steps in random directions. It is known that for dimensions $d = 2$ and $d = 4$ , all the…

math.CO2025

Emerging consecutive pattern avoidance

Nathanaël Hassler, Sergey Kirgizov

In this note we study the asymptotic popularity, that is, the limit probability to find a given consecutive pattern at a random position in a random permutation in the eighteen cla…

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.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

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.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

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,…

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…

math.CO2021

Asymptotic bit frequency in Fibonacci words

Jean-Luc Baril, Sergey Kirgizov, Vincent Vajnovszki

It is known that binary words containing no $k$ consecutive 1s are enumerated by $k$ -step Fibonacci numbers. In this note we discuss the expected value of a random bit in a random…

math.CO2021★ 1 cited

Bijections from Dyck and Motzkin meanders with catastrophes to pattern avoiding Dyck paths

Jean-Luc Baril, Sergey Kirgizov

In this note, we present constructive bijections from Dyck and Motzkin meanders with catastrophes to Dyck paths avoiding some patterns. As a byproduct, we deduce correspondences fr…

math.CO2021

Transformation à la Foata for special kinds of descents and excedances

Jean-Luc Baril, Sergey Kirgizov

A pure excedance in a permutation $π = π_{1} π_{2} \dots π_{n}$ is a position $i < π_{i}$ such that there is no $j < i$ with $i \leq π_{j} < π_{i}$ . We present a one-to-one correspondence on the symmetr…

math.CO2020

Pattern statistics in faro words and permutations

Jean-Luc Baril, Alexander Burstein, Sergey Kirgizov

We study the distribution and the popularity of some patterns in $k$ -ary faro words, i.e. words over the alphabet ${1, 2, \dots, k}$ obtained by interlacing the letters of two n…

math.CO2019

Pattern distributions in Dyck paths with a first return decomposition constrained by height

Jean-Luc Baril, Richard Genestier, Sergey Kirgizov

We provide generating functions for the popularity and the distribution of patterns of length at most three over the set of Dyck paths having a first return decomposition constrain…

math.CO2019

Bijections between directed animals, multisets and Grand-Dyck paths

Jean-Luc Baril, David Bevan, Sergey Kirgizov

An $n$ -multiset of $[k] = {1, 2, \dots, k}$ consists of a set of $n$ elements from $[k]$ where each element can be repeated. We present the bivariate generating function for $n$ -mul…

math.CO2018

Enumeration of Łukasiewicz paths modulo some patterns

Jean-Luc Baril, Sergey Kirgizov, Armen Petrossian

For any pattern $α$ of length at most two, we enumerate equivalence classes of Łukasiewicz paths of length $n \geq 0$ where two paths are equivalent whenever the occurrence position…

math.CO2018

Descent distribution on Catalan words avoiding a pattern of length at most three

Jean-Luc Baril, Sergey Kirgizov, Vincent Vajnovszki

Catalan words are particular growth-restricted words over the set of non-negative integers, and they represent still another combinatorial class counted by the Catalan numbers. We…

Brick Wall Excursions: Combinatorial Interpretation of Random Flight Moments

Emerging consecutive pattern avoidance

Enumeration in the lattice of q-decreasing words

The ascent lattice on Dyck paths

Grand zigzag knight's paths

The Combinatorics of Motzkin Polyominoes

A lattice on Dyck paths close to the Tamari lattice

Grand Dyck paths with air pockets

Dyck paths with catastrophes modulo the positions of a given pattern

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

Asymptotic bit frequency in Fibonacci words

Bijections from Dyck and Motzkin meanders with catastrophes to pattern avoiding Dyck paths

Transformation à la Foata for special kinds of descents and excedances

Pattern statistics in faro words and permutations

Pattern distributions in Dyck paths with a first return decomposition constrained by height

Bijections between directed animals, multisets and Grand-Dyck paths

Enumeration of Łukasiewicz paths modulo some patterns

Descent distribution on Catalan words avoiding a pattern of length at most three

Enumeration in the lattice of $q$ -decreasing words