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@Article{fang-bipartite,
  author  = {Fang, W.},
  title   = {Bijective link between {C}hapoton's new intervals and bipartite planar maps},
  journal = {European J. Combin.},
  year    = {2021},
  volume  = {97},
  pages   = {Article 103382},
  doi     = {10.1016/j.ejc.2021.103382},
}

@Article{BMS,
  author     = {Bousquet-M{\'e}lou, M. and Schaeffer, G.},
  title      = {Enumeration of planar constellations},
  journal    = {Adv. in Appl. Math.},
  year       = {2000},
  volume     = {24},
  number     = {4},
  pages      = {337--368},
  issn       = {0196-8858},
  doi        = {10.1006/aama.1999.0673},
  fjournal   = {Advances in Applied Mathematics},
  mrclass    = {05A15 (05C05 05C30 57M12)},
  mrnumber   = {1761777 (2001g:05006)},
  mrreviewer = {Volker Strehl},
  url        = {http://dx.doi.org/10.1006/aama.1999.0673},
}

@Article{BDFG,
  author   = {Bouttier, J. and Di Francesco, P. and Guitter, E.},
  title    = {Planar maps as labeled mobiles},
  journal  = {Electron. J. Combin.},
  year     = {2004},
  volume   = {11},
  number   = {1},
  pages    = {Research Paper 69, 27},
  issn     = {1077-8926},
  doi      = {10.37236/1822},
  fjournal = {Electronic Journal of Combinatorics},
  mrclass  = {05C30 (05A15 05C05 82B41)},
  mrnumber = {2097335 (2005i:05087)},
  url      = {http://www.combinatorics.org/Volume_11/Abstracts/v11i1r69.html},
}

@Article{desc-tree,
  author     = {Cori, R. and Schaeffer, G.},
  title      = {Description trees and {T}utte formulas},
  journal    = {Theoret. Comput. Sci.},
  year       = {2003},
  volume     = {292},
  number     = {1},
  pages      = {165--183},
  issn       = {0304-3975},
  note       = {Selected papers in honor of Jean Berstel},
  coden      = {TCSDI},
  doi        = {10.1016/S0304-3975(01)00221-3},
  fjournal   = {Theoretical Computer Science},
  mrclass    = {05C30 (05A15 05C05 05C10 68R10)},
  mrnumber   = {1964632},
  mrreviewer = {W. G. Brown},
  url        = {http://dx.doi.org/10.1016/S0304-3975(01)00221-3},
}

@Article{planar-lambda,
  author    = {Zeilberger, N and Giorgetti, A.},
  title     = {A correspondence between rooted planar maps and normal planar lambda terms},
  journal   = {Log. Methods Comput. Sci.},
  year      = {2015},
  volume    = {11},
  number    = {3},
  pages     = {1--39},
  doi       = {10.2168/LMCS-11(3:22)2015},
  publisher = {Centre pour la Communication Scientifique Directe ({CCSD})},
}

@Article{fusy-bij,
  author     = {Fusy, {\'E}.},
  title      = {New bijective links on planar maps via orientations},
  journal    = {European J. Combin.},
  year       = {2010},
  volume     = {31},
  number     = {1},
  pages      = {145--160},
  issn       = {0195-6698},
  doi        = {10.1016/j.ejc.2009.02.008},
  fjournal   = {European Journal of Combinatorics},
  mrclass    = {05C30 (05A19 05C10)},
  mrnumber   = {2552598},
  mrreviewer = {Catherine H. Yan},
  url        = {http://dx.doi.org/10.1016/j.ejc.2009.02.008},
}

@Article{walsh-lehman,
  author     = {Walsh, T. R. S. and Lehman, A. B.},
  title      = {Counting rooted maps by genus. {III}: {N}onseparable maps},
  journal    = {J. Combin. Theory Ser. B},
  year       = {1975},
  volume     = {18},
  pages      = {222--259},
  fjournal   = {Journal of Combinatorial Theory. Series B},
  mrclass    = {05C30},
  mrnumber   = {0373954},
  mrreviewer = {W. G. Brown},
}

@Article{wormald,
  author     = {Wormald, N. C.},
  title      = {A correspondence for rooted planar maps},
  journal    = {Ars Combin.},
  year       = {1980},
  volume     = {9},
  pages      = {11--28},
  issn       = {0381-7032},
  coden      = {ACOMDN},
  fjournal   = {Ars Combinatoria},
  mrclass    = {05C30},
  mrnumber   = {582273},
  mrreviewer = {R. C. Entringer},
}

@Article{lambda-cubic,
  author    = {Bodini, O. and Gardy, D. and Jacquot, A.},
  title     = {Asymptotics and random sampling for {BCI} and {BCK} lambda terms},
  journal   = {Theoret. Comput. Sci.},
  year      = {2013},
  volume    = {502},
  pages     = {227--238},
  doi       = {10.1016/j.tcs.2013.01.008},
  publisher = {Elsevier},
}

@Article{lambda-trivalent,
  author    = {Zeilberger, N.},
  title     = {Linear lambda terms as invariants of rooted trivalent maps},
  journal   = {J. Funct. Program.},
  year      = {2016},
  volume    = {26},
  doi       = {10.1017/S095679681600023X},
  publisher = {Cambridge University Press},
}

@Article{chord-diagram-bridgeless,
  author  = {Courtiel, J. and Yeats, K. and Zeilberger, N.},
  title   = {Connected chord diagrams and bridgeless maps},
  journal = {Electron. J. Combin.},
  year    = {2019},
  doi     = {10.48550/arXiv.1611.04611},
}

@Article{Tutte-census,
  author     = {Tutte, W. T.},
  title      = {A census of planar maps},
  journal    = {Canad. J. Math.},
  year       = {1963},
  volume     = {15},
  pages      = {249--271},
  issn       = {0008-414X},
  doi        = {10.4153/CJM-1963-029-x},
  fjournal   = {Canadian Journal of Mathematics. Journal Canadien de Math\'ematiques},
  mrclass    = {55.10},
  mrnumber   = {0146823 (26 \#4343)},
  mrreviewer = {G. de B. Robinson},
  publisher  = {Canadian Mathematical Society},
}

@Article{sticky,
  author  = {Fang, W.},
  title   = {Planar triangulations, bridgeless planar maps and {T}amari intervals},
  journal = {European J. Combin.},
  year    = {2018},
  volume  = {70},
  pages   = {75--91},
  issn    = {0195-6698},
  doi     = {10.1016/j.ejc.2017.12.002},
}

@Article{nonsep,
  author  = {Fang, W. and Pr{\'e}ville-Ratelle, L.-F.},
  title   = {The enumeration of generalized {T}amari intervals},
  journal = {European J. Combin.},
  year    = {2017},
  volume  = {61},
  pages   = {69--84},
  doi     = {10.1016/j.ejc.2016.10.003},
}

@Article{bipartite-root-degree,
  author  = {Liskovets, V. A.},
  title   = {A pattern of asymptotic vertex valency distributions in planar maps},
  journal = {J. Combin. Theory Ser. B},
  year    = {1999},
  volume  = {75},
  pages   = {116--133},
}

@Article{BMJ,
  author     = {Bousquet-M{\'e}lou, M. and Jehanne, A.},
  title      = {Polynomial equations with one catalytic variable, algebraic series and map enumeration},
  journal    = {J. Combin. Theory Ser. B},
  year       = {2006},
  volume     = {96},
  number     = {5},
  pages      = {623--672},
  issn       = {0095-8956},
  coden      = {JCBTB8},
  doi        = {10.1016/j.jctb.2005.12.003},
  fjournal   = {Journal of Combinatorial Theory. Series B},
  mrclass    = {05A15 (05C30)},
  mrnumber   = {2236503 (2008e:05005)},
  mrreviewer = {Daniel Brown},
  url        = {http://dx.doi.org/10.1016/j.jctb.2005.12.003},
}

@Article{cf-bipartite,
  author  = {Chapuy, G. and Fang, W.},
  title   = {Generating Functions of Bipartite Maps on Orientable Surfaces},
  journal = {Electron. J. Combin.},
  year    = {2016},
  volume  = {23},
  number  = {3},
  pages   = {P3.31},
  doi     = {10.37236/5511},
}

@InProceedings{imploid,
  author    = {Zeilberger, N.},
  title     = {A theory of linear typings as flows on 3-valent graphs},
  booktitle = {Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science},
  year      = {2018},
  pages     = {919--928},
}

@Misc{grygiel-yu,
  author = {Grygiel, K. and Yu, G.-R.},
  title  = {In search of a bijection between $\beta$-normal 3-indecomposable planar lambda terms and $\beta(0,1)$-trees},
  year   = {2020},
  note   = {Talk in the 15th workshop of Computational Logic and Applications (CLA 2020)},
  url    = {https://cla.tcs.uj.edu.pl/pdfs/CLA_slides_Grygiel-Yu.pdf},
}

@Misc{3-conn-conj,
  author = {Zeilberger, N. and Reed, J.},
  title  = {Some topological properties of planar lambda terms},
  year   = {2019},
  note   = {Talk in the 14th workshop of Computational Logic and Applications (CLA 2019)},
  url    = {https://cla.tcs.uj.edu.pl/history/2019/slides/Zeilberger.pdf},
}

@Article{generalized-BCI,
  author  = {Bodini, O. and Gardy, D. and Gittenberger, B. and Jacquot, A.},
  title   = {Enumeration of generalized {BCI} {L}ambda-terms},
  journal = {Electron. J. Combin.},
  year    = {2013},
  volume  = {20},
  number  = {4},
  pages   = {P30},
  doi     = {10.37236/3051},
}

@Article{tamari-calculus,
  author  = {Zeilberger, N.},
  title   = {A sequent calculus for a semi-associative law},
  journal = {Log. Methods Comput. Sci.},
  year    = {2019},
  volume  = {15},
  number  = {1},
  pages   = {9:1-- 9:23},
  doi     = {10.23638/LMCS-15(1:9)2019},
}

@Article{lambda-stat,
  author  = {Bendkowski, M. and Bodini, O. and Dovgal, S.},
  title   = {Statistical Properties of Lambda Terms},
  journal = {Electron. J. Combin.},
  year    = {2019},
  volume  = {26},
  number  = {4},
  pages   = {P4.1},
}

@Misc{linear-stat,
  author     = {Bodini, O. and Singh, A. and Zeilberger, N.},
  title      = {Asymptotic distribution of parameters in trivalent maps and linear lambda terms},
  year       = {2021},
  eprint     = {2106.08291},
  eprinttype = {arxiv},
}

@InProceedings{description-tree,
  author    = {Cori, R. and Jacquard, B. and Schaeffer, G.},
  title     = {Description trees for some families of planar maps},
  booktitle = {Proceedings of the 9th conference on formal power series and algebraic combinatorics},
  year      = {1997},
}

@Misc{full-version,
  author      = {Wenjie Fang},
  title       = {Bijections between planar maps and planar linear normal $\lambda$-terms with connectivity condition},
  year        = {2022},
  eprint      = {2202.03542},
  eprintclass = {math.CO},
  eprinttype  = {arxiv},
  keywords    = {math.CO, cs.LO},
}

@Comment{jabref-meta: databaseType:bibtex;}