The ascent lattice on Dyck paths
Jean-Luc Baril, Mireille Bousquet-Mélou, Sergey Kirgizov, Mehdi Naima
pdf arXiv, accepted to The Electronic Journal of Combinatorics, 2025

Asymptotics of self-overlapping permutations
Sergey Kirgizov and Khaydar Nurligareev
pdf arXiv, Discrete Mathematics, 348(5), 2025

Endhered patterns in matchings and RNA
Célia Biane, Greg Hampikian, Sergey Kirgizov, Khaydar Nurligareev
pdf arXiv, Journal of Computational Biology, 32(1), 2025

The combinatorics of Motzkin polyominoes
Jean-Luc Baril, Sergey Kirgizov, José Luis Ramírez, Diego Villamizar
pdf arXiv, Discrete Applied Mathematics, 364, 2025

Distribution of endhered patterns in RNA-related secondary structures
Célia Biane, Greg Hampikian, Sergey Kirgizov, Khaydar Nurligareev, Daniel Pinson
Presented by Sk at SeqBIM 2024, slides.pdf, booklet of abstracts

Grand zigzag knight’s paths
Jean-Luc Baril, Nathanaël Hassler, Sergey Kirgizov and José Luis Ramírez
pdf arXiv, Enumerative combinatorics and applications, 5(1), 2025.

Asymptotic of consecutive patterns in permutations and matchings
Célia Biane, Khaydar Nurligareev, Sergey Kirgizov
Video of the talk, slides in pdf
Presented by Khaydar Nurligareev
Al-Khwarizmi Applied Mathematics Webinar, September 2024

The combinatorics of Motzkin polyominoes abstract
Jean-Luc Baril, Sergey Kirgizov, José L. Ramírez and Diego Villamizar
Presented by Diego Villamizar from Universidad Sergio Arboleda (Colombia)
ICECA, International Conference Enumerative Combinatorics and Applications, University of Haifa, Virtual, August 26-28, 2024

Motifs en combinatoire slides
Sergey Kirgizov
Assemblée générale du LIB, 4 Juillet 2024, Dijon

L’art et la combinatoire slides
Sergey et Yulia Kirgizova
Journée Arts Design et Sciences, 30 mai 2024, Dijon

Asymptotics of endhered patterns in perfect matchings
Célia Biane, Khaydar Nurligareev, Sergey Kirgizov
Presented by Khaydar at ALEA Days, Journées ALEA, March 11-15, 2024, Marseille

Grand zigzag knight’s paths
Jean-Luc Baril, Nathanaël Hassler, Sergey Kirgizov, José L. Ramírez
Presented by Nathanaël at ALEA Days, Journées ALEA, March 11-15, 2024, Marseille

Sturm meets Fibonacci in Minkowski’s fractal bar
Sergey Kirgizov and Sergey Dovgal
Presented at Permutation Patterns 2023, Dijon, France, July 3-7, 2023
See the slides!

In July 2023 we organized Permutation patterns conference in Dijon.

Grand Dyck paths with air pockets
Jean-Luc Baril, Sergey Kirgizov, Rémi Maréchal, and Vincent Vajnovszki
pdf arXiv. The Art of Discrete and Applied Mathematics, 7(1), 2023.

Rémi presented our joint work at ALEA Days, Journées ALEA, March 13-17, 2023.
An introduction to Dyck paths with air pockets
Jean-Luc Baril, Sergey Kirgizov, Rémi Maréchal and Vincent Vajnovszki

Enumeration of Dyck paths with air pockets
Jean-Luc Baril, Sergey Kirgizov, Rémi Maréchal, and Vincent Vajnovszki
pdf arXiv. Journal of Integer Sequences, 26, 2023.

Q-bonacci words and numbers
Sergey Kirgizov
pdf arXiv. Presented at The Twentieth International Conference on Fibonacci Numbers and Their Applications, (slides) The Fibonacci Quarterly, 60(5), 2022

Polyominoes and graphs built from Fibonacci words
Sergey Kirgizov and José Luis Ramírez
pdf arXiv. The Fibonacci Quarterly, 60(5), 2022

Fibonacci q-decreasing words: enumerative results and Gray codes
Joint work with Jean-Luc Baril and Vincent Vajnovszki
Preseted by Vincent at AUA-UAEU Workshop on Graph Theory, Combinatorics and Applications (GTCA), Al Ain — UAE, November 13-15, 2022.

Dyck paths with catastrophes modulo the positions of a given pattern
Jean-Luc Baril, Sergey Kirgizov, Armen Petrossian
pdf arXiv. Australasian Journal of Combinatorics, Volume 84, Issue 3, 2022

This was presented at The Twentieth International Conference on Fibonacci Numbers and Their Applications. Super!

La conferenza GASCom2022 è stata fantastica!
Lì incontro molte persone meravigliose e gentili :)
Ho presentato il mio lavoro congiunto con Jean-Luc Baril e Vincent Vajnovszki, guarda le diapositive! Si prega di consultare le nostre diapositive e l’articolo pubblicato su una rivista scientifica PU.M.A. nel giugno 2022.

Gray codes for Fibonacci q-decreasing words
Jean-Luc Baril, Sergey Kirgizov and Vincent Vajnovszki
pdf arXiv. Theoretical Computer Science, available online 6 June 2022

Helmut Prodinger applied a kernel method to enumerate partial Dyck paths with air pockets. Dyck paths with air pockets were recently introduced by our team (Baril, Kirgizov, Maréchal, Vajnovszki), February 2022. I like the how the Helmut’s paper starts: "In a paper that was posted on valentine’s day [1], Baril et al. introduced a new family of Dyck-like paths, called Dyck paths with air pockets."

Lattice paths with a first return decomposition constrained by the maximal height of a pattern
Jean-Luc Baril and Sergey Kirgizov
pdf arXiv is published in Discrete Mathematics Letters, Volume 8, 2022.

Our paper Clique percolation method: memory efficient almost exact communities pdf arXiv
written together with Alexis Baudin, Maximilien Danisch, Sergey Kirgizov, Clémence Magnien and Marwan Ghanem
presented by Alexis at 17th anniversary of the International Conference on Advanced Data Mining and Applications, (ADMA’21), Sydney, Australia, 2-4 February, 2022

Qubonacci words
Permutations patterns 2021, June 15-16
Joint work with Jean-Luc Baril and Vincent Vajnovszki
Look at my slides, and one page abstract of our work.
Conf photos (click to enlarge) :

Pattern statistics in faro words and permutations
Jean-Luc Baril, Alexander Burstein and Sergey Kirgizov
pdf arXiv is published in Discrete Mathematics, Volume 344, Issue 8, August 2021

Bijections from Dyck and Motzkin meanders with catastrophes to pattern avoiding Dyck paths pdf arXiv
Jean-Luc Baril and Sergey Kirgizov
is published in Discrete Mathematics Letters, Volume 7, 2021.

Our paper Gray codes for Fibonacci q-decreasing words solved a conjecture of Ömer Eğecioğlua (Santa Barbara, California) and Vesna Iršič (Ljubljana, Slovenia) from their recently published paper Fibonacci-run graphs I: Basic properties (31 May 2021).

Paper Transformation à la Foata for special kinds of descents and excedances pdf
is published in Enumerative Combinatorics and Applications, 2021, arXiv
Written together with Jean-Luc Baril.

The combinatorial community is awesome! On March 24, 2021, Bin Han, Jianxi Mao, Jiang Zeng anounced the proof of our second conjecture from this paper. The first conjecture remains open.

Our lab LIB participated in art-science exhibition "Les Réseaunautes",
presented from March 15, 2021 until April 26, 2021 in Darcy garden, downtown of Dijon, France.



You may wish to follow the links to see more photos or check out the posters.
Consider also the main page of the ArtScience biennial “Réseaux ! Partout tu tisses”.

Pattern distribution in faro words and permutations
Permutations patterns 2020, June 30 - July 1
Look at a .pdf poster, a short video (5 min) and a two page abstract of our joint work with Jean-Luc Baril
Check out these magnificient conference photos (click to enlarge) :

Vive les équations des motifs et les équations des statistiques !
Pattern distributions in Dyck paths with a first return decomposition constrained by height pdf arXiv
Discrete Mathematics, Volume 343, Issue 9, September 2020
Jean-Luc Baril, Richard Genestier and Sergey Kirgizov

Paper Bijections between directed animals, multisets and Grand-Dyck paths pdf
is published in The Electronic Journal of Combinatorics Volume 27, Issue 2 (2020), Article P2.10
arXiv
Jean-Luc Baril, David Bevan and Sergey Kirgizov

Talk. Temporal density of community structure.
MARAMI 2019, Dijon, 8 Novembre 2019.
Look at our slides and the presentation video (21 min).
Joint work, together with Éric Leclercq

Motzkin paths with a restricted first return decomposition pdf
INTEGERS 19, September 2019
Jean-Luc Baril, Sergey Kirgizov and Armen Petrossian

I’m the Maître de conférences now !!!

Enumeration of Łukasiewicz paths modulo some patterns pdf
Discrete Mathematics, Volume 342, Issue 4, April 2019
Jean-Luc Baril, Sergey Kirgizov and Armen Petrossian

Descent distribution on Catalan words avoiding a pattern of length at most three pdf Discrete Mathematics, Volume 341, Issue 9, September 2018
Jean-Luc Baril, Sergey Kirgizov and Vincent Vajnovszki
arXiv

A paper Dyck paths with a first return decomposition constrained by height is published! pdf
Discrete Mathematics 341(6): 1620-1628 (2018)
Jean-Luc Baril, Sergey Kirgizov and Armen Petrossian

In June 2017 I was in Iceland, presenting our poster about Forests and pattern avoiding permutations modulo pure descents in Permutation Patterns Conference at Reykjavik University.

Our paper intitled Un observatoire pour la modélisation et l’analyse des réseaux multi-relationnels. Une application à l’étude du discours politique sur Twitter .htm written together with Ian Basaille, Eric Leclercq, Marinette Savonnet, Nadine Cullot, Thierry Grison, Elisabeth Gavignet
is publised in Document Numérique 20(1): 101-136 (2017)

Our paper about reinforcement learning for autonomic resource allocation in clouds was re-presented by Muthu Karunarathna in series of students seminars organised by Eiko Yoneki in the Computer Laboratory, University of Cambridge. The original paper was presented at Seventh International Conference on Autonomic and Autonomous Systems, ICAS 2011 and received a Best Paper Award.