@misc{FFN24, title={Tamari intervals and blossoming trees}, author={Fang, Wenjie and Fusy, {\' E}ric and Nadeau, Philippe}, year={2024}, eprint={2312.13159}, archivePrefix={arXiv}, primaryClass={math.CO} } @Misc{full, author = {Enrica Duchi and Gilles Schaeffer}, title = {From order one catalytic decompositions to context-free specifications, bijectively}, eprint={2412.20628}, archivePrefix={arXiv}, year = 2024, note = {Submitted}} @InProceedings{S23, author = {Gilles Schaeffer}, title = {On universal singular exponents in equations with one catalytic parameter of order one}, year = 2023, booktitle = {EuroComb}, address = {Prague, Czech Republicg}, doi = {10.5817/CZ.MUNI.EUROCOMB23-111}, pages = {806--811}} @InProceedings{DuHe, author = {Enrica Duchi and Corentin Henriet}, title = {Combinatorics of fighting fish, planar maps and Tamari intervals}, booktitle = {FPSAC, Bengalore. Séminaire Lotharingien de Combinatoire}, year = 2022, number = {86B.83}} @Unpublished{DS, author = {Enrica Duchi and Gilles Schaeffer}, title = {From }, note = {}, OPTkey = {}, OPTmonth = {}, OPTyear = {}, OPTannote = {} } @inproceedings{BCKN20, author = {Alin Bostan and Arnaud Carayol and Florent Koechlin and Cyril Nicaud}, editor = {Artur Czumaj and Anuj Dawar and Emanuela Merelli}, title = {Weakly-Unambiguous Parikh Automata and Their Link to Holonomic Series}, booktitle = {47th International Colloquium on Automata, Languages, and Programming, {ICALP} 2020, July 8-11, 2020, Saarbr{\"{u}}cken, Germany (Virtual Conference)}, series = {LIPIcs}, volume = 168, pages = {114:1--114:16}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum f{\"{u}}r Informatik}, year = 2020, url = {https://doi.org/10.4230/LIPIcs.ICALP.2020.114}, doi = {10.4230/LIPIcs.ICALP.2020.114}, timestamp = {Mon, 21 Dec 2020 13:23:22 +0100}, biburl = {https://dblp.org/rec/conf/icalp/BostanCKN20.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} } @misc{LC, author = {Chen, Linxiao}, keywords = {Combinatorics (math.CO), Probability (math.PR), FOS: Mathematics, FOS: Mathematics, 05A16 (Primary) 05A15, 05C05, 82B26 (Secondary)}, title = {Enumeration of fully parked trees}, eprinttype = {arXiv}, eprint = {2103.15770}, year = 2021, } @Misc{C-M2, author = {Chapuy, Guillaume}, title = {Combinatoire d'objets planaires via leurs fonctions génératrices}, howpublished = {Mémoire de M2}, year = 2006} @InProceedings{DH, author = {Drmota, Michael and Hainzl, Eva-Maria}, title = {{Universal Properties of Catalytic Variable Equations}}, booktitle = {AofA}, pages = {7:1--7:15}, series = {LIPIcs}, year = {2022}, volume = {225}, } @InProceedings{DH-full, author = {Drmota, Michael and Hainzl, Eva-Maria}, title = {{Universal Properties of Catalytic Variable Equations}}, booktitle = {33rd International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2022)}, pages = {7:1--7:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-230-3}, ISSN = {1868-8969}, year = {2022}, volume = {225}, editor = {Ward, Mark Daniel}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/opus/volltexte/2022/16093}, URN = {urn:nbn:de:0030-drops-160930}, doi = {10.4230/LIPIcs.AofA.2022.7}, annote = {Keywords: catalytic equation, singular expansion, univeral asymptotics} } @InProceedings{BCNSED, AUTHOR = {Bostan, Alin and Chyzak, Fr\'ed\'eric and Notarantonio, Hadrien and El Din, Mohab Safey}, TITLE = {Algorithms for discrete differential equations of order 1}, BOOKTITLE = {I{SSAC} '22---{P}roceedings of the 2022 {I}nternational {S}ymposium on {S}ymbolic and {A}lgebraic {C}omputation}, PAGES = {101--110}, PUBLISHER = {ACM, New York}, YEAR = {[2022] \copyright 2022}, } @Book{Harrison, author = {Michael Harrison}, title = {Introduction to Formal Language Theory}, publisher = {Addison-Wesley}, year = 1978 } @Misc{Chen, key = {Enumeration of fully parked trees}, author = {Linxiao Chen}, title = {Enumeration of fully parked trees}, year = 2021, eprint={2103.15770}, eprinttype={arXiv}, } @book{FS, AUTHOR = {Flajolet, Philippe and Sedgewick, Robert}, TITLE = {Analytic combinatorics}, PUBLISHER = {Cambridge University Press, Cambridge}, YEAR = {2009}, PAGES = {xiv+810 pp.}, DOI = {10.1017/CBO9780511801655}, URL = {https://doi.org/10.1017/CBO9780511801655}, } @misc{sportiello2021boltzmann, title={Boltzmann sampling of irreducible context-free structures in linear time}, author={Andrea Sportiello}, year={2021}, eprint={2105.12881}, archivePrefix={arXiv}, primaryClass={math.CO} } @article{gs:DuFlLoSc04, Author = {Duchon, Philippe and Flajolet, Philippe and Louchard, Guy and Schaeffer, Gilles }, Date-Modified = {2009-03-03 06:46:52 +0100}, Journal = {Combin. Probab. Comput.}, Keywords = {random generation, Boltzmann samplers}, Local-Url = {file://localhost/Users/fusy/Dropbox/Boulot/Bibli/Numerise/DuFlLoSc03.pdf}, Note = {Special issue on Analysis of Algorithms.}, Number = {4--5}, Pages = {577--625}, Title = {Boltzmann Samplers for the Random Generation of Combinatorial Structures}, Volume = 13, Year = 2004} @InCollection{chomsky_schutzenberger, author = {Chomsky, Noam and Schützenberger, Marcel-Paul}, title = {The Algebraic Theory of Context-Free Languages}, editor = {P. Braffort and D. Hirschberg}, booktitle = {Computer Programming and Formal Systems}, publisher = {North-Holland}, year = 1963, pages = {118-161}} @article{DELEST1984169, title = {Algebraic languages and polyominoes enumeration}, journal = {Theoretical Computer Science}, volume = {34}, number = {1}, pages = {169-206}, year = {1984}, issn = {0304-3975}, doi = {https://doi.org/10.1016/0304-3975(84)90116-6}, url = {https://www.sciencedirect.com/science/article/pii/0304397584901166}, author = {Marie-Pierre Delest and Gérard Viennot}, } @incollection{gs:BM-ICM, AUTHOR = {Bousquet-M\'elou, Mireille}, TITLE = {Rational and algebraic series in combinatorial enumeration}, BOOKTITLE = {International {C}ongress of {M}athematicians. {V}ol. {III}}, PAGES = {789--826}, PUBLISHER = {Eur. Math. Soc., Z\"urich}, YEAR = {2006}, } @article{ChyzakYeats-2020-BBL, author = {Chyzak, Frédéric and Yeats, Karen}, title = {Bijections between {Ł}ukasiewicz walks and generalized tandem walks}, journal = {The Electronic Journal of Combinatorics}, volume = {27}, number = {2}, month = apr, year = 2020, note = {Article number P2.3. 46 pages. Implementation available at \url{https://arxiv.org/abs/1810.04117}}, doi = {10.37236/8261}, urlpdf = {http://specfun.inria.fr/chyzak/Publications/ChyzakYeats-2020-BBL.pdf} } @Article{BD, author = {Banderier, Cyril and Drmota, Michael}, title = {Formulae and asymptotics for coefficients of algebraic functions}, journal = { Combinatorics, Probability and Computing}, year = 2015, volume = 24, pages = {1--53}} @article{FLAJOLET1987283, title = {Analytic models and ambiguity of context-free languages}, journal = {Theoretical Computer Science}, volume = {49}, number = {2}, pages = {283-309}, year = {1987}, issn = {0304-3975}, doi = {https://doi.org/10.1016/0304-3975(87)90011-9}, url = {https://www.sciencedirect.com/science/article/pii/0304397587900119}, author = {Philippe Flajolet} } @article{BMJ, author = {Mireille Bousquet{-}M{\'{e}}lou and Arnaud Jehanne}, title = {Polynomial equations with one catalytic variable, algebraic series and map enumeration}, journal = {J. Comb. Theory, Ser. {B}}, volume = {96}, number = {5}, pages = {623--672}, year = {2006}, DOI = {10.1016/j.jctb.2005.12.003}, } @article{FANG2020111802, AUTHOR = {Fang, Wenjie}, TITLE = {A partial order on {M}otzkin paths}, JOURNAL = {Discrete Math.}, FJOURNAL = {Discrete Mathematics}, VOLUME = {343}, YEAR = {2020}, NUMBER = {5}, PAGES = {111802, 9 pp.}, DOI = {10.1016/j.disc.2019.111802}, URL = {https://doi.org/10.1016/j.disc.2019.111802}, } @article{DNY, AUTHOR = {Drmota, Michael and Noy, Marc and Yu, Guan-Ru}, TITLE = {Universal singular exponents in catalytic variable equations}, JOURNAL = {J. Combin. Theory Ser. A}, FJOURNAL = {Journal of Combinatorial Theory. Series A}, VOLUME = {185}, YEAR = {2022}, PAGES = {Paper No. 105522, 33 pp.}, DOI = {10.1016/j.jcta.2021.105522}, URL = {https://doi.org/10.1016/j.jcta.2021.105522}, } @article{BOUSQUETMELOU20161171, title = {An elementary solution of Gessel's walks in the quadrant}, journal = {Advances in Mathematics}, volume = {303}, pages = {1171-1189}, year = {2016}, issn = {0001-8708}, doi = {https://doi.org/10.1016/j.aim.2016.08.038}, url = {https://www.sciencedirect.com/science/article/pii/S0001870815302735}, author = {Mireille Bousquet-Mélou}, } @Article{bostan-rachel, author = {Bostan, A.; Kurkova, I.; Raschel, K.}, title = { A human proof of Gessel's lattice path conjecture}, journal = {Trans. Amer. Math. Soc.}, year = 2017, volume = 369, number = 2, pages = {1365--1393}} @article{Zeilberger-Giorgetti, AUTHOR = {Zeilberger, Noam and Giorgetti, Alain}, TITLE = {A correspondence between rooted planar maps and normal planar lambda terms}, JOURNAL = {Log. Methods Comput. Sci.}, FJOURNAL = {Logical Methods in Computer Science}, VOLUME = {11}, YEAR = {2015}, NUMBER = {3}, PAGES = {3:22, 39 pp.}, DOI = {10.2168/LMCS-11(3:22)2015}, URL = {https://doi.org/10.2168/LMCS-11(3:22)2015}, } @article{BODINI2013227, title = {Asymptotics and random sampling for BCI and BCK lambda terms}, journal = {Theoretical Computer Science}, volume = {502}, pages = {227-238}, year = {2013}, note = {Generation of Combinatorial Structures}, issn = {0304-3975}, doi = {https://doi.org/10.1016/j.tcs.2013.01.008}, url = {https://www.sciencedirect.com/science/article/pii/S0304397513000583}, author = {O. Bodini and D. Gardy and A. Jacquot}, } @article{GIZ, author = {Katarzyna Grygiel and Pawel M. Idziak and Marek Zaionc}, title = {How big is {BCI} fragment of {BCK} logic}, journal = {J. Log. Comput.}, volume = {23}, number = {3}, pages = {673--691}, year = {2013}, url = {https://doi.org/10.1093/logcom/exs017}, doi = {10.1093/logcom/exs017}, timestamp = {Wed, 17 May 2017 14:25:55 +0200}, biburl = {https://dblp.org/rec/journals/logcom/GrygielIZ13.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} } @InCollection{chapterMaps, AUTHOR = {Schaeffer, Gilles}, TITLE = {Planar maps}, BOOKTITLE = {Handbook of enumerative combinatorics}, SERIES = {Discrete Math. Appl. (Boca Raton)}, PAGES = {335--395}, PUBLISHER = {CRC Press, Boca Raton, FL}, YEAR = {2015}, } @Article{bouttier2021bijective, AUTHOR = {Bouttier, J\'er\'emie and Guitter, Emmanuel and Miermont, Gr\'egory}, TITLE = {Bijective enumeration of planar bipartite maps with three tight boundaries, or how to slice pairs of pants}, JOURNAL = {Ann. H. Lebesgue}, FJOURNAL = {Annales Henri Lebesgue}, VOLUME = {5}, YEAR = {2022}, PAGES = {1035--1110}, DOI = {10.5802/ahl.143}, URL = {https://doi.org/10.5802/ahl.143}, } @book{AST_1975__27__1_0, AUTHOR = {Cori, Robert}, TITLE = {Un code pour les graphes planaires et ses applications}, SERIES = {Ast\'erisque}, VOLUME = {No. 27}, PUBLISHER = {Soci\'et\'e{} Math\'ematique de France, Paris}, YEAR = {1975}, PAGES = {i+169}, url = {http://www.numdam.org/item/AST_1975__27__1_0/} } @Misc{cori, author = {Cori, Robert}, howpublished = {personnal communication}} @article{ALCO_2020__3_2_433_0, AUTHOR = {Chapoton, Fr\'ed\'eric}, TITLE = {Some properties of a new partial order on {D}yck paths}, JOURNAL = {Algebr. Comb.}, FJOURNAL = {Algebraic Combinatorics}, VOLUME = {3}, YEAR = {2020}, NUMBER = {2}, PAGES = {433--463}, DOI = {10.5802/alco.98}, URL = {https://doi.org/10.5802/alco.98}, } @Article{chapoton, AUTHOR = {Chapoton, F.}, TITLE = {Sur le nombre d'intervalles dans les treillis de {T}amari}, JOURNAL = {S\'em. Lothar. Combin.}, FJOURNAL = {S\'eminaire Lotharingien de Combinatoire}, VOLUME = {55}, YEAR = {2005/07}, PAGES = {Art. B55f, 18 pp.}, } @article{GW, AUTHOR = {Goulden, I. P. and West, J.}, TITLE = {Raney paths and a combinatorial relationship between rooted nonseparable planar maps and two-stack-sortable permutations}, JOURNAL = {J. Combin. Theory Ser. A}, FJOURNAL = {Journal of Combinatorial Theory. Series A}, VOLUME = {75}, YEAR = {1996}, NUMBER = {2}, PAGES = {220--242}, DOI = {10.1006/jcta.1996.0074}, URL = {https://doi.org/10.1006/jcta.1996.0074}, } @article{dulucq1998combinatorial, title={A combinatorial proof of J. West's conjecture}, author={Dulucq, Serge and Gire, Sophie and Guibert, Olivier}, journal={Discrete Mathematics}, volume={187}, number={1-3}, pages={71--96}, year={1998}, publisher={Elsevier} } @article{claesson, author = {Claesson, Anders and Kitaev, Sergey and Steingr\'{\i}msson, Einar}, title = {Decompositions and Statistics for Beta(1,0)-Trees and Nonseparable Permutations}, year = {2009}, issue_date = {March, 2009}, publisher = {Academic Press, Inc.}, address = {USA}, volume = {42}, number = {3}, issn = {0196-8858}, url = {https://doi.org/10.1016/j.aam.2008.09.001}, doi = {10.1016/j.aam.2008.09.001}, journal = {Adv. Appl. Math.}, month = mar, pages = {313–328}, numpages = {16}, } @book{moharthomassen, title={Graphs on Surfaces}, author={Mohar, B. and Thomassen, C.}, isbn={9780801866890}, lccn={lc00048799}, series={Johns Hopkins Studies in Nineteenth C Architecture Series}, year={2001}, publisher={Johns Hopkins University Press} } @article{physics, title={2D gravity and random matrices}, volume={254}, ISSN={0370-1573}, url={http://dx.doi.org/10.1016/0370-1573(94)00084-G}, DOI={10.1016/0370-1573(94)00084-g}, number={1-2}, journal={Physics Reports}, publisher={Elsevier BV}, author={Francesco, P.Di and Ginsparg, P. and Zinn-Justin, J.}, year={1995}, month={Mar}, pages={1–133} } @article{gs:R99, Author = {Rossignac, J.}, Date-Modified = {2007-04-17 15:22:49 +0200}, Journal = {IEEE Transactions on Visualization and Computer Graphics}, Keywords = {meshes, encoding}, Number = 1, Pages = {47--61}, Title = {Edgebreaker: Connectivity Compression for Triangle Meshes.}, Volume = 5, Year = 1999} @article{gs:Sc97, Author = {Schaeffer, G.}, Date-Modified = {2007-04-18 11:13:11 +0200}, Journal = {Electron. J. Combin.}, Keywords = {bijections, blossoming trees, maps, eulerian maps}, Local-Url = {file://localhost/Users/fusy/Dropbox/Boulot/Bibli/Numerise/v4i1r20.pdf}, Number = {1}, Pages = {\string# 20, 14 pp.}, Title = {Bijective census and random generation of {E}ulerian planar maps with prescribed vertex degrees}, Volume = {4}, Year = {1997}} @incollection{gs:Sc99, Address = {New York}, Author = {Schaeffer, G.}, Booktitle = {Proceedings of the ACM Symposium on Theory of Computing (Atlanta, GA, 1999)}, Date-Modified = {2009-03-03 07:27:54 +0100}, Keywords = {random generation, maps}, Local-Url = {file://localhost/Users/fusy/Dropbox/Boulot/Bibli/Numerise/Sc99.pdf}, Pages = {760--769 (electronic)}, Publisher = {ACM}, Title = {Random sampling of large planar maps and convex polyhedra}, Year = {1999}} @article{gs:PS03b, Author = {Poulalhon, D. and Schaeffer, G. }, Date-Modified = {2009-09-19 08:31:44 +0200}, Journal = {Algorithmica}, Keywords = {encoding, triangulations}, Local-Url = {file://localhost/Users/fusy/Dropbox/Boulot/Bibli/Numerise/PoSc03.pdf}, Pages = {505-527}, Title = {Optimal Coding and Sampling of Triangulations}, Volume = {46(3-4)}, Year = {2006}} @article{gs:FuPoScL, Author = {Fusy, \'E. and Poulalhon, D. and Schaeffer, G. }, Date-Modified = {2007-12-01 07:17:37 +0100}, Journal = {Transactions on Algorithms}, Keywords = {maps, 3-connected maps, orientations, realizors, random generation, encoding, bijections}, Month = {April}, Number = {2}, Pages = {Art. 19}, Title = {Dissections, orientations, and trees, with applications to optimal mesh encoding and to random sampling}, Volume = {4}, Year = {2008}} @article{LG13, title={Uniqueness and universality of the Brownian map}, author={Le Gall, Jean-Fran{\c{c}}ois}, journal={The Annals of Probability}, volume={41}, number={4}, pages={2880--2960}, year={2013}, publisher={Institute of Mathematical Statistics} } @article{M13, title={The Brownian map is the scaling limit of uniform random plane quadrangulations}, author={Miermont, Gr{\'e}gory}, journal={Acta mathematica}, volume={210}, number={2}, pages={319--401}, year={2013}, publisher={Institut Mittag-Leffler} }@article{PPS, title = {Algorithms for combinatorial structures: Well-founded systems and Newton iterations}, journal = {Journal of Combinatorial Theory, Series A}, volume = {119}, number = {8}, pages = {1711-1773}, year = {2012}, issn = {0097-3165}, doi = {https://doi.org/10.1016/j.jcta.2012.05.007}, url = {https://www.sciencedirect.com/science/article/pii/S0097316512000908}, author = {Carine Pivoteau and Bruno Salvy and Michèle Soria}, keywords = {Species theory, Analytic combinatorics, Newton iteration, Generating functions, Complexity}, } @article{cori-schaeffer, title = {Description trees and Tutte formulas}, JOURNAL = {Theoret. Comput. Sci.}, FJOURNAL = {Theoretical Computer Science}, volume = {292}, number = {1}, pages = {165-183}, year = {2003}, note = {Selected Papers in honor of Jean Berstel}, issn = {0304-3975}, doi = {https://doi.org/10.1016/S0304-3975(01)00221-3}, url = {https://www.sciencedirect.com/science/article/pii/S0304397501002213}, author = {Robert Cori and Gilles Schaeffer}, keywords = {Enumeration, Trees, Planar maps, Quadratic method}, abstract = {In this paper we introduce and enumerate families of description trees. These families of trees consist of plane trees in which the nodes are labelled by nonnegative integers, and where the label of each node satisfies a condition relating it to the labels of its sons. We give a recursive construction of these trees which translates simply in an equation for their generating function. By solving this equation via the quadratic method introduced by Brown and Tutte, we prove that this generating function is algebraic. For some families the number of trees we obtain is equal to the numbers given by Tutte to enumerate different kinds of planar maps. We provide bijections between description trees and corresponding families of planar maps to explain these equalities. Description trees are instances of objects that can be described by description operators; we conjecture that such families of objects have algebraic generating functions. They were find also to be related to the enumeration of pattern avoiding permutations.} } @article{cori-richard, title = {Enumeration des graphes planaires a l'aide des series formelles en variables non commutatives}, journal = {Discrete Mathematics}, volume = {2}, number = {2}, pages = {115-162}, year = {1972}, issn = {0012-365X}, doi = {https://doi.org/10.1016/0012-365X(72)90080-5}, url = {https://www.sciencedirect.com/science/article/pii/0012365X72900805}, author = {Robert Cori and Jean Richard}, abstract = {Résumé L'énumération des grapises planaires a été developpée par W.T. Tutte et son école. Nous abordons le sujet par des moyens tout à fait différents' nous établissons une bijection entre les graphes planaires et un langage formel. Des relations vérifiées par ce langage formel dans l'algebre des sous-ensembles d'un monoide libre, nous déduisons des équations avec opérateur pour des séries formelles en variables non commutatives. Ce sont des séries génératrices pour graphes planaires; de cette facon, une théorie de ces équations nous permet de donner des formules d'énumérations.} } @article{Contat23, AUTHOR = {Contat, Alice}, TITLE = {Parking on trees with a (random) given degree sequence and the frozen configuration model}, JOURNAL = {Electron. J. Probab.}, FJOURNAL = {Electronic Journal of Probability}, VOLUME = {30}, YEAR = {2025}, PAGES = {Paper No. 37, 25 pp.}, DOI = {10.1214/25-ejp1290}, URL = {https://doi.org/10.1214/25-ejp1290}, } @Article{contat24, author = {Alice Contat}, title = {Last car decomposition of planar maps}, journal = {Ann. Inst. Henri Poincaré Comb. Phys. Interact.}, year = 2024} @Article{contatcurien21, author = {Alice Contat and Nicolas Curien}, title = {Parking on Cayley trees \& Frozen Erdős-Rényi}, journal = {The Annals of Probability}, year = 2021} @misc{chencontat24, author = {Linxiao Chen and Alice Contat}, title = {Parking on supercritical geometric Bienaymé--Galton--Watson trees}, year = 2024, url = {https://arxiv.org/abs/2402.05612} } @article{Pan, AUTHOR = {Lackner, Marie-Louise and Panholzer, Alois}, TITLE = {Parking functions for mappings}, JOURNAL = {J. Combin. Theory Ser. A}, FJOURNAL = {Journal of Combinatorial Theory. Series A}, VOLUME = {142}, YEAR = {2016}, PAGES = {1--28}, MRREVIEWER = {Valery\ A.\ Liskovets}, DOI = {10.1016/j.jcta.2016.03.001}, URL = {https://doi.org/10.1016/j.jcta.2016.03.001}, }