% Encoding: UTF-8 @InProceedings{AsinowskiBanderier20, AUTHOR={Asinowski, Andrei and Banderier, Cyril}, TITLE={Generating functions and multivariate Gaussian distribution for lattice paths with marked patterns (extended abstract)}, booktitle={Proceedings of AofA'20}, booktitle_notused = {31th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA'20)}, year = {2020}, volume_notused = {159}, series_notused = {Leibniz International Proceedings in Informatics (LIPIcs)}, pages = {24.1--24.15}, url = {https://lipn.univ-paris13.fr/~banderier/Papers/AsinowskiBanderier2020.pdf}, address= {Klagenfurt, Austria}, doi_notused={10.4230/LIPIcs.AofA.2020.24}, } @Article{NoonanZeilberger99, Author = {Noonan, John and Zeilberger, Doron}, Title = {{The Goulden--Jackson cluster method: Extensions, applications and implementations}}, FJournal = {{Journal of Difference Equations and Applications}}, Journal = {{J. Difference Equ. 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Appl.}, PAGES = {589--678}, PUBLISHER = {CRC Press}, YEAR = {2015}, url={https://arxiv.org/pdf/1503.05930}, doi_notused={dx.doi.org/10.1201/b18255-13}, } @article{Riordan75, author = {Riordan, John}, title = {Enumeration of Plane Trees by Branches and Endpoints}, journal = {J. Comb. Theory, Ser. {A}}, volume = {19}, number = {2}, pages = {214--222}, year = {1975}, url = {https://doi.org/10.1016/S0097-3165(75)80010-0}, DOI_notused = {10.1016/S0097-3165(75)80010-0}, biburl = {https://dblp.org/rec/bib/journals/jct/Riordan75}, } @article {Sulanke03, AUTHOR = {Sulanke, Robert A.}, TITLE = {Objects counted by the central {D}elannoy numbers}, JOURNAL = {J. 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Integer Seq.}, year = {2006}, volume = {9}, number = {3}, pages = {Article 06.3.2, 8~pp.}, issn_notused = {1530-7638}, fjournal = {Journal of Integer Sequences}, url = {https://cs.uwaterloo.ca/journals/JIS/VOL9/Parviainen/parviainen3.pdf}, } %% Reference related to OEIS A162551 @incollection {PanRemmel19, AUTHOR = {Pan, Ran and Remmel, Jeffrey B.}, TITLE = {Paired patterns in lattices paths}, BOOKTITLE = {Lattice paths combinatorics and applications}, SERIES = {Developments in Mathematics Series}, pages = {382--418}, PUBLISHER = {Springer}, YEAR = {2019}, url={https://arxiv.org/pdf/1601.07988}, } %% Several references on "dispersed Dyck paths" @Article{HacklHeubergerProdinger18, author = {{Hackl}, Benjamin and {Heuberger}, Clemens and {Prodinger}, Helmut}, title = {Ascents in non-negative lattice paths}, journal = {arXiv}, note_notused={will perhaps be submitted this summer 2019 (dixit Benjamin)}, note={Long version of \textit{Counting Ascents in Generalized Dyck Paths}, published in the Analysis of Algorithms'2018 proceedings}, year = {2018}, month = jan, url={https://arxiv.org/pdf/1801.02996}, } @Article{Callan04, author = {Callan, David}, title = {Some bijections for restricted Motzkin paths}, journal = {arXiv:math/0407374}, year = {2004}, month = jul, url={https://arxiv.org/pdf/math/0407374.pdf}, } @article {KangroPourmoradnasseriTheis16, AUTHOR = {Kangro, Kairi and Pourmoradnasseri, Mozhgan and Theis, Dirk Oliver}, TITLE = {Short note on the number of 1-ascents in dispersed {D}yck paths}, JOURNAL = {Discrete Math. Algorithms Appl.}, FJOURNAL = {Discrete Mathematics, Algorithms and Applications}, VOLUME = {9}, YEAR = {2017}, NUMBER = {6}, PAGES = {1750077, 8}, issn_notused = {1793-8309}, DOI_notused = {10.1142/S179383091750077X}, URL = {https://arxiv.org/pdf/1603.01422}, } @Article{BarilKirgizovPetrossian18, author = {{Baril}, Jean-Luc and {Kirgizov}, Sergey and {Petrossian}, Armen}, title = {{Enumeration of {\L}ukasiewicz paths modulo some patterns}}, journal = {Discrete Math.}, fjournal = {Discrete Mathematics}, year = {2019}, number={4}, volume={342}, pages={997--1005}, doi_notused={10.1016/j.disc.2018.12.005}, url={https://arxiv.org/pdf/1804.01293.pdf}, } @Article{Carlson21, author = {Carlson, Fritz}, title = {{\"Uber {P}otenzreihen mit ganzzahligen {K}oeffizienten}}, journal = {Math. 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Math. Theor. Comp. Sci.}}, FJOURNAL = {{Discrete Mathematics \& Theoretical Computer Science}}, VOLUME_notused = {{DMTCS Proceedings vol. AM, 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10)}}, volume={AM}, YEAR = {2010}, MONTH = Jan, } @InProceedings{AsinowskiBacherBanderierGittenberger18a, author = {Asinowski, Andrei and Bacher, Axel and Banderier, Cyril and Gittenberger, Bernhard}, title = {Analytic combinatorics of lattice paths with forbidden patterns: enumerative aspects}, booktitle = {Language and Automata Theory and Applications. 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Erster Band: Reihen, Integralrechnung, Funktionentheorie}}, publisher = {Springer}, year = {1925}, author = {P{\'o}lya, George and Szeg\H{o}, G{\'a}bor}, edition = {1st}, isbn = {978-3-662-37599-0,978-3-662-38381-0}, url = {http://gen.lib.rus.ec/book/index.php?md5=bc15c3ed52d2e94dc32336160568cc67}, } % series = {Die Grundlehren der Mathematischen Wissenschaften 20}, @Book{MadrasSlade13, title = {{The Self-avoiding Walk}}, publisher = {Birkh\"auser/Springer}, year = {2013}, author = {Madras, Neal and Slade, Gordon}, series = {Modern Birkh\"auser Classics}, isbn = {978-1-4614-6024-4; 978-1-4614-6025-1}, note = {Reprint of the 1993 original}, doi = {10.1007/978-1-4614-6025-1}, pages = {xvi+425}, } @Book{Stanley11, title = {Enumerative {C}ombinatorics. {V}ol. 1}, publisher = {Cambridge University Press}, year = {2011}, author = {Stanley, Richard P.}, volume = {49}, series = {Cambridge Studies in Advanced Mathematics}, edition = {2nd}, pages = {xiv+626}, url={http://www-math.mit.edu/~rstan/ec/ec1.pdf}, ISBN = {978-1-107-60262-5}, } @Book{Stanley99, title = {Enumerative {C}ombinatorics. {V}ol. 2}, publisher = {Cambridge University Press}, year = {1999}, author = {Stanley, Richard P.}, volume = {62}, series = {Cambridge Studies in Advanced Mathematics}, address = {Cambridge}, isbn = {0-521-56069-1; 0-521-78987-7}, note = {With a foreword by Gian-Carlo Rota and appendix 1 by Sergey Fomin}, doi = {10.1017/CBO9780511609589}, pages = {xii+581}, } @Book{PolyaSzego98, title = {{Problems and Theorems in Analysis.} {I}}, publisher = {Springer-Verlag}, year = {1998}, author = {P{\'o}lya, George and Szeg{\H{o}}, Gabor}, series = {Classics in Mathematics}, note = {Series, integral calculus, theory of functions, Translated from the German by Dorothee Aeppli, Reprint of the 1978 English translation}, mrclass = {00A07 (01A75)}, mrnumber = {1492447}, pages = {xx+389}, } @Article{Cramer38, author = {Cram{\'e}r, Harald}, title = {Sur un nouveau th{\'e}or{\`e}me-limite de la th{\'e}orie de probabilit{\'e}s}, journal = {Actualit{\'e}s {S}cientifiques et {I}ndustrielles}, year = {1938}, volume = {736}, pages = {5--23}, } @Article{Drmota94, author = {Drmota, Michael}, title = {A bivariate asymptotic expansion of coefficients of powers of generating functions}, journal = {European J. 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Moon}, } @Article{Wallner16, author = {Wallner, Michael}, title = {A half-normal distribution scheme for generating functions}, journal = {arXiv preprint arXiv:1610.00541}, year = {2016}, } @PhdThesis{Wallner16a, author = {Michael Wallner}, title = {Combinatorics of Lattice Paths and Tree-Like Structures}, school = {Technische Universit\"at Wien}, year = {2016}, address = {Austria, Vienna}, month = {December}, } @Book{Dieudonne71, title = {{Infinitesimal Calculus}}, publisher = {Hermann, Paris; Houghton Mifflin Co., Boston, Mass.}, year = {1971}, author = {Dieudonn\'e, Jean}, note = {Translated from the French}, mrclass = {00A05}, mrnumber = {0349286}, pages = {427}, } @Book{Dieudonne80, title = {Calcul infinit\'esimal}, publisher = {Hermann, Paris}, year = {1980}, author = {Dieudonn\'e, Jean}, edition = {2}, note = {1st edition in 1968: 479pp., there is also an English translation of the 1st edition in 1971, 427pp.}, pages = {482}, } @Book{Abhyankar90a, title = {{Algebraic Geometry for Scientists and Engineers}}, publisher = {American Mathematical Society}, year = {1990}, author = {Abhyankar, Shreeram S.}, volume = {35}, series = {Mathematical Surveys and Monographs}, isbn = {0-8218-1535-0}, doi = {10.1090/surv/035}, pages = {xiv+295}, } @Book{Kirwan92, title = {{Complex Algebraic Curves}}, publisher = {Cambridge University Press, Cambridge}, year = {1992}, author = {Kirwan, Frances}, volume = {23}, series = {London Mathematical Society Student Texts}, isbn = {0-521-41251-X; 0-521-42353-8}, doi = {10.1017/CBO9780511623929}, pages = {viii+264}, } @Article{Raney60, author = {Raney, George Neal}, title = {Functional composition patterns and power series reversion}, journal = {Trans. Amer. Math. Soc.}, year = {1960}, volume = {94}, pages = {441--451}, issn_notused = {0002-9947}, doi = {10.2307/1993433}, fjournal = {Transactions of the American Mathematical Society}, mrclass = {05.00 (40.00)}, mrnumber = {0114765}, mrreviewer = {Rimhak Ree}, } @Article{DvoretzkyMotzkin47, author = {Dvoretzky, A. and Motzkin, Th.}, title = {A problem of arrangements}, journal = {Duke Math. J.}, year = {1947}, volume = {14}, pages = {305--313}, issn_notused = {0012-7094}, fjournal = {Duke Mathematical Journal}, url = {http://projecteuclid.org/euclid.dmj/1077474127}, } @Article{Majumdar10, author = {Majumdar, Satya N.}, title = {Universal first-passage properties of discrete-time random walks and {L}\'evy flights on a line: statistics of the global maximum and records}, journal = {Phys. A}, year = {2010}, volume = {389}, number = {20}, pages = {4299--4316}, issn_notused = {0378-4371}, doi = {10.1016/j.physa.2010.01.021}, fjournal = {Physica A. Statistical Mechanics and its Applications}, mrclass = {60G50 (62G32 82C31)}, mrnumber = {2673925}, } @Article{Marchal98, author = {Marchal, Philippe}, title = {Distribution of the occupation time for a {L}\'evy process at passage times at {$0$}}, journal = {Stochastic Process. Appl.}, year = {1998}, volume = {74}, number = {1}, pages = {123--131}, issn_notused = {0304-4149}, doi = {10.1016/S0304-4149(97)00106-3}, fjournal = {Stochastic Processes and their Applications}, mrclass = {60J30 (60J55)}, mrnumber = {1624021}, mrreviewer = {Patrick Fitzsimmons}, } @Article{Minton14, author = {Minton, Gregory T.}, title = {Linear recurrence sequences satisfying congruence conditions}, journal = {Proc. Amer. Math. Soc.}, year = {2014}, volume = {142}, number = {7}, pages = {2337--2352}, issn_notused = {0002-9939}, doi = {10.1090/S0002-9939-2014-12168-X}, fjournal = {Proceedings of the American Mathematical Society}, mrclass = {11B50 (11A07 11B37 11R04 11R45)}, mrnumber = {3195758}, mrreviewer = {W. Narkiewicz}, } @Article{BacherBousquet-Melou11, author = {Bacher, Axel and Bousquet-M\'elou, Mireille}, title = {Weakly directed self-avoiding walks}, journal = {Journal of Combinatorial Theory, Series A}, year = {2011}, volume = {118}, number = {8}, pages = {2365--2391}, issn_notused = {0097-3165}, doi_notused = {10.1016/j.jcta.2011.06.001}, keywords = {Enumeration, Self-avoiding walks, Partially directed bridges, Non-D-finite series, Random generation}, url={https://www.sciencedirect.com/science/article/pii/S0097316511001002/pdf}, } @InCollection{ChomskySchuetzenberger63, author = {Chomsky, Noam and Sch\"utzenberger, Marcel-Paul}, title = {The algebraic theory of context-free languages}, booktitle = {Computer programming and formal systems}, publisher = {North-Holland, Amsterdam}, year = {1963}, pages = {118--161}, doi_notused = {10.1016/S0049-237X(08)72023-8}, mrclass = {94.50 (68.00)}, mrnumber = {0152391}, mrreviewer = {E. Shamir}, url={http://www-igm.univ-mlv.fr/~berstel/Mps/Travaux/A/1963-7ChomskyAlgebraic.pdf}, } @Article{Schuetzenberger63, author = {Sch\"utzenberger, Marcel-Paul}, title = {On context-free languages and push-down automata}, journal = {Information and Control}, year = {1963}, volume = {6}, pages = {246--264}, issn_notused = {0890-5401}, doi_notused = {10.1016/S0019-9958(63)90306-1}, url={https://www.sciencedirect.com/science/article/pii/S0019995863903061/pdf}, fjournal = {Information and Computation}, } @InCollection{Bousquet-Melou06, author = {Bousquet-M\'elou, Mireille}, title = {Rational and algebraic series in combinatorial enumeration}, booktitle = {International {C}ongress of {M}athematicians. {V}ol. {III}}, publisher = {EMS}, year = {2006}, pages = {789--826}, url = {https://hal.archives-ouvertes.fr/file/index/docid/277255/filename/icm.pdf}, } %publisher = {Eur. Math. Soc., Z\"urich}, @Article{Bousquet-Melou08, author = {Bousquet-M\'elou, Mireille}, title = {Discrete excursions}, journal = {S\'em. Lothar. Combin.}, year = {2008}, volume = {57}, pages = {Article~B57d, 23~pp.}, issn_notused = {1286-4889}, fjournal = {S\'eminaire Lotharingien de Combinatoire}, url={http://www.emis.de/journals/SLC/wpapers/s57bousquet.pdf}, } @Article{Duchon00, author = {Duchon, Philippe}, title = {On the enumeration and generation of generalized {D}yck words}, journal = {Discrete Math.}, fjournal = {Discrete Mathematics}, year = {2000}, volume = {225}, number = {1-3}, pages = {121--135}, issn_notused = {0012-365X}, doi_notused = {10.1016/S0012-365X(00)00150-3}, url={https://www.sciencedirect.com/science/article/pii/S0012365X00001503}, } %note = {Formal power series and algebraic combinatorics (Toronto, 1998)}, @Article{LabelleYeh90, author = {Labelle, Jacques and Yeh, Yeong-Nan}, title = {Generalized {D}yck paths}, journal = {Discrete Math.}, fjournal = {Discrete Mathematics}, year = {1990}, volume = {82}, number = {1}, pages = {1--6}, issn_notused = {0012-365X}, not_used = {10.1016/0012-365X(90)90039-K}, url={https://www.sciencedirect.com/science/article/pii/0012365X9090039K}, } @Article{MerliniRogersSprugnoliVerri99, author = {Merlini, Donatella and Rogers, Douglas G. and Sprugnoli, Renzo and Verri, Maria Cecilia}, title = {Underdiagonal lattice paths with unrestricted steps}, journal = {Discrete Appl. Math.}, year = {1999}, volume = {91}, number = {1-3}, pages = {197--213}, issn_notused = {0166-218X}, doi_notused = {10.1016/S0166-218X(98)00126-7}, fjournal = {Discrete Applied Mathematics. The Journal of Combinatorial Algorithms, Informatics and Computational Sciences}, url={https://www.sciencedirect.com/science/article/pii/S0166218X98001267/pdf}, } @Article{GuibasOdlyzko81, author = {Guibas, Leonidas J. and Odlyzko, Andrew M.}, title = {String overlaps, pattern matching, and nontransitive games}, journal = {J. Combin. Theory Ser. A}, year = {1981}, volume = {30}, number = {2}, pages = {183--208}, issn_notused = {0097-3165}, doi_notused = {10.1016/0097-3165(81)90005-4}, fjournal = {Journal of Combinatorial Theory. Series A}, url={https://www.sciencedirect.com/science/article/pii/0097316581900054/pdf}, } @Article{HofackerReidysStadler12, author = {Hofacker, Ivo L. and Reidys, Christian M. and Stadler, Peter F.}, title = {Symmetric circular matchings and {RNA} folding}, journal = {Discrete Math.}, year = {2012}, volume = {312}, number = {1}, pages = {100--112}, issn_notused = {0012-365X}, doi_notused = {10.1016/j.disc.2011.06.004}, fjournal = {Discrete Mathematics}, url={https://www.sciencedirect.com/science/article/pii/S0012365X11002615/pdf}, } @Article{Baril16, author = {Baril, Jean-Luc}, title = {Avoiding patterns in irreducible permutations}, journal = {Discrete Math. Theor. Comput. Sci.}, year = {2016}, volume = {17}, number = {3}, pages = {13--30}, issn_notused = {1365-8050}, fjournal = {Discrete Mathematics \& Theoretical Computer Science.}, url = {http://jl.baril.u-bourgogne.fr/vincular.pdf}, } @Article{Mansour06, author = {Mansour, Toufik}, title = {Statistics on {D}yck paths}, journal = {J. Integer Seq.}, year = {2006}, volume = {9}, number= {1}, pages = {Article 06.1.5, 13~pp.}, issn_notused = {1530-7638}, fjournal = {Journal of Integer Sequences}, mrclass = {05A15}, mrnumber = {2193155}, mrreviewer = {Anna de Mier}, url = {https://cs.uwaterloo.ca/journals/JIS/VOL9/Mansour/mansour86.pdf}, } % number = {1}, @Article{BonaKnopfmacher10, author = {B\'ona, Mikl\'os and Knopfmacher, Arnold}, title = {On the probability that certain compositions have the same number of parts}, journal = {Ann. Comb.}, year = {2010}, volume = {14}, number = {3}, pages = {291--306}, issn_notused = {0218-0006}, doi = {10.1007/s00026-010-0060-7}, fjournal = {Annals of Combinatorics}, } @Article{JinReidys08b, author = {Jin, Emma Y. and Reidys, Christian M.}, title = {Asymptotic enumeration of {RNA} structures with pseudoknots}, journal = {Bull. Math. Biol.}, year = {2008}, volume = {70}, number = {4}, pages = {951--970}, issn_notused = {0092-8240}, doi_notused = {10.1007/s11538-007-9265-2}, fjournal = {Bulletin of Mathematical Biology}, url={https://arxiv.org/abs/0706.3137}, } @article {JinReidys08, AUTHOR = {Jin, Emma Y. and Qin, Jing and Reidys, Christian M.}, TITLE = {Combinatorics of {RNA} structures with pseudoknots}, JOURNAL = {Bull. Math. Biol.}, FJOURNAL = {Bulletin of Mathematical Biology}, VOLUME = {70}, YEAR = {2008}, NUMBER = {1}, PAGES = {45--67}, issn_notused = {0092-8240}, DOI_notused = {10.1007/s11538-007-9240-y}, URL = {https://arxiv.org/abs/0704.2518}, } @Article{Sun04, author = {Sun, Yidong}, title = {The statistic ``number of {\it udu}'s'' in {D}yck paths}, journal = {Discrete Math.}, year = {2004}, volume = {287}, number = {1-3}, pages = {177--186}, issn_notused = {0012-365X}, doi_notused = {10.1016/j.disc.2004.07.002}, fjournal = {Discrete Mathematics}, url={https://www.sciencedirect.com/science/article/pii/S0012365X04003036/pdf}, } @Article{Righi10, author = {Righi, C\'eline}, title = {Number of ``{$udu$}''s of a {D}yck path and ad-nilpotent ideals of parabolic subalgebras of {${\rm sl}_{l+1}({\mathbb{C}})$}}, journal = {S\'em. Lothar. 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