@article{GLMN16,
    author = {Giraudo, S. and Luque, J.-G. and Mignot, L. and Nicart, F.},
    title = {{Operads, quasiorders, and regular languages}},
    journal = {Adv. Appl. Math.},
    volume = {75},
    pages = {56--93},
    year = {2016}
}


@article {Solomon1976,
    AUTHOR = {Solomon, Louis},
     TITLE = {A {M}ackey formula in the group ring of a {C}oxeter group},
   JOURNAL = {J. Algebra},
  FJOURNAL = {J. Algebra},
    VOLUME = {41},
      YEAR = {1976},
    NUMBER = {2},
     PAGES = {255--264},
   MRCLASS = {20C05},
  MRNUMBER = {444756},
MRREVIEWER = {Gerald O. Losey},
       DOI = {10.1016/0021-8693(76)90182-4},
       URL = {https://doi.org/10.1016/0021-8693(76)90182-4},
}

@incollection {BBG1990,
    AUTHOR = {Bergeron, F. and Bergeron, N. and Garsia, A. M.},
     TITLE = {Idempotents for the free {L}ie algebra and {$q$}-enumeration},
 BOOKTITLE = {Invariant theory and tableaux ({M}inneapolis, {MN}, 1988)},
    SERIES = {IMA Vol. Math. Appl.},
    VOLUME = {19},
     PAGES = {166--190},
 PUBLISHER = {Springer, New York},
      YEAR = {1990},
   MRCLASS = {17B01 (05A15 05A30 05E10)},
  MRNUMBER = {1035495},
MRREVIEWER = {Ira Gessel},
}

@book {CR2006,
    AUTHOR = {Curtis, Charles W. and Reiner, Irving},
     TITLE = {Representation theory of finite groups and associative
              algebras},
      NOTE = {Reprint of the 1962 original},
 PUBLISHER = {AMS Chelsea Publishing, Providence, RI},
      YEAR = {2006},
     PAGES = {xiv+689},
   MRCLASS = {16-02 (20-02 20Cxx)},
  MRNUMBER = {2215618},
       DOI = {10.1090/chel/356},
       URL = {https://doi.org/10.1090/chel/356},
}

@book {BS2005,
    AUTHOR = {Blessenohl, Dieter and Schocker, Manfred},
     TITLE = {Noncommutative character theory of the symmetric group},
 PUBLISHER = {Imperial College Press, London},
      YEAR = {2005},
     PAGES = {x+172},
   MRCLASS = {20C30 (05E05 05E10 16S34)},
  MRNUMBER = {2424338},
MRREVIEWER = {Jeb F. Willenbring},
       DOI = {10.1142/p369},
       URL = {https://doi.org/10.1142/p369},
}

@article {BB1992,
    AUTHOR = {Bergeron, F. and Bergeron, N.},
     TITLE = {A decomposition of the descent algebra of the hyperoctahedral
              group. {I}},
   JOURNAL = {J. Algebra},
  FJOURNAL = {Journal of Algebra},
    VOLUME = {148},
      YEAR = {1992},
    NUMBER = {1},
     PAGES = {86--97},
   MRCLASS = {20F55 (05E99 17B01)},
  MRNUMBER = {1161567},
MRREVIEWER = {John R. Stembridge},
       DOI = {10.1016/0021-8693(92)90238-H},
       URL = {https://doi.org/10.1016/0021-8693(92)90238-H},
}

@article {GR1989,
    AUTHOR = {Garsia, A. M. and Reutenauer, C.},
     TITLE = {A decomposition of {S}olomon's descent algebra},
   JOURNAL = {Adv. Math.},
  FJOURNAL = {Adv. Math.},
    VOLUME = {77},
      YEAR = {1989},
    NUMBER = {2},
     PAGES = {189--262},
   MRCLASS = {20C05 (05E10 17B01 20C30)},
  MRNUMBER = {1020585},
MRREVIEWER = {Ira Gessel},
       DOI = {10.1016/0001-8708(89)90020-0},
       URL = {https://doi.org/10.1016/0001-8708(89)90020-0},
}

@incollection{Garsia1990,
  title={Combinatorics of the free Lie algebra and the symmetric group},
  author={Garsia, Adriano M},
  booktitle={Analysis, et cetera},
  pages={309--382},
  year={1990},
  publisher={Elsevier}
}

@inproceedings{Dynkin1947,
  title={Absch{\"a}tzung der Koeffizienten der Campbell-Hausdorff-Formel},
  author={Dynkin, EB},
  booktitle={Dokl. Akad. Nauk USSR},
  volume={57},
  pages={323--326},
  year={1947}
}

@article{Ree1958,
  title={Lie elements and an algebra associated with shuffles},
  author={Ree, Rimhak},
  journal={Annals of Mathematics},
  pages={210--220},
  year={1958},
  publisher={JSTOR}
}

@incollection{Reutenauer1986,
  title={Theorem of Poincar{\'e}-Birkhoff-Witt, logarithm and symmetric group representations of degrees equal to Stirling numbers},
  author={Reutenauer, Christophe},
  booktitle={Combinatoire {\'e}num{\'e}rative},
  pages={267--284},
  year={1986},
  publisher={Springer}
}

@misc{Reutenauer1993,
  title={Free Lie Algebras. Clarendon},
  author={Reutenauer, Christophe},
  year={1993},
  publisher={Oxford}
}

@article{DynkinCH,
  title={Calculation of the coefficients in the Campbell--Hausdorff formula},
  author={Dynkin, EB},
  journal={DYNKIN, EB Selected Papers of EB Dynkin with Commentary. Ed. by YUSHKEVICH, AA},
  pages={31--35},
  year={2000}
}

@article{Dynkin1949,
  title={On the representation by means of commutators of the series $\backslash$log(e\^{}xe\^{}y) for noncommutative x and y},
  author={Dynkin, Evgenii Borisovich},
  journal={Matematicheskii Sbornik},
  volume={67},
  number={1},
  pages={155--162},
  year={1949},
  publisher={Russian Academy of Sciences, Steklov Mathematical Institute of Russian~…}
}

@article{Specht1948,
  title={Die linearen Beziehungen zwischen h{\"o}heren Kommutatoren},
  author={Specht, Wilhelm},
  journal={Mathematische Zeitschrift},
  volume={51},
  number={3},
  pages={367--376},
  year={1948},
  publisher={Springer}
}

@article{Wever1947,
  title={{\"u}ber Invarianten in Lie'schen Ringen},
  author={Wever, Franz},
  journal={Mathematische Annalen},
  volume={120},
  number={1},
  pages={563--580},
  year={1947},
  publisher={Springer}
}

@article{BL1991,
  title={On the coefficients in the associative expansion of a Lie word},
  author={Blessenohl, Dieter and Laue, Hartmut},
  journal={European Journal of Combinatorics},
  volume={12},
  number={3},
  pages={205--210},
  year={1991},
  publisher={Academic Press}
}

@article{MR1995,
    AUTHOR = {Malvenuto, Clauda and Reutenauer, Christophe},
     TITLE = {Duality between quasi-symmetric functions and the {S}olomon
              descent algebra},
   JOURNAL = {J. Algebra},
  FJOURNAL = {Journal of Algebra},
    VOLUME = {177},
      YEAR = {1995},
    NUMBER = {3},
     PAGES = {967--982}, 
       DOI = {10.1006/jabr.1995.1336}, 
}

@article{FQSym,
  title={Noncommutative symmetric functions},
  author={Gelfand, Israel and Krob, Daniel and Lascoux, Alain and Leclerc, Bernard and Retakh, Vladimir S and Thibon, J-Y},
  journal={arXiv preprint hep-th/9407124},
  year={1994}
}

@article{AS2005,
  title={Structure of the Malvenuto--Reutenauer Hopf algebra of permutations},
  author={Aguiar, Marcelo and Sottile, Frank},
  journal={Adv. Math.},
  volume={191},
  number={2},
  pages={225--275},
  year={2005},
  publisher={Elsevier}
}

@article{LR1998,
    AUTHOR = {Loday, Jean-Louis and Ronco, Mar\'ia O.},
     TITLE = {Hopf algebra of the planar binary trees},
   JOURNAL = {Adv. Math.},
  FJOURNAL = {Advances in Mathematics},
    VOLUME = {139},
      YEAR = {1998},
    NUMBER = {2},
     PAGES = {293--309}, 
       DOI = {10.1006/aima.1998.1759}, 
}

@article{LR2002,
  title={Order structure on the algebra of permutations and of planar binary trees},
  author={Loday, Jean-Louis and Ronco, Mar{\'\i}a O},
  journal={Journal of Algebraic Combinatorics},
  volume={15},
  number={3},
  pages={253--270},
  year={2002},
  publisher={Springer}
}

@incollection{Barratt1978,
  title={Twisted Lie algebras},
  author={Barratt, Michael G},
  booktitle={Geometric Applications of Homotopy Theory II},
  pages={9--15},
  year={1978},
  publisher={Springer}
}

@article{AL2007,
  title={The associative operad and the weak order on the symmetric groups},
  author={Aguiar, Marcelo and Livernet, Muriel},
  journal={J. Homotopy Relat. Str.},
  volume={2},
  number={1},
  pages={57--84},
  year={2007}
}

@article{DLPR2020,
  title={Areas of areas generate the shuffle algebra},
  author={Diehl, Joscha and Lyons, Terry and Prei{\ss}, Rosa and Reizenstein, Jeremy},
  journal={arXiv preprint arXiv:2002.02338},
  year={2020}
}

@article{FP2013,
  title={Natural endomorphisms of shuffle algebras},
  author={Foissy, Lo{\"\i}c and Patras, Fr{\'e}d{\'e}ric},
  journal={International Journal of Algebra and Computation},
  volume={23},
  number={04},
  pages={989--1009},
  year={2013},
  publisher={World Scientific}
}

@article{Chapoton2002,
  title={Construction de certaines op{\'e}rades et bigebres associ{\'e}es aux polytopes de Stasheff et hypercubes},
  author={Chapoton, Fr{\'e}d{\'e}ric},
  journal={Trans. Am. Math. Soc.},
  volume={354},
  number={1},
  pages={63--74},
  year={2002},
       DOI = {10.1090/S0002-9947-01-02809-4},
}

@article{YV2022,
  title={Algebraic structure of the Hopf algebra of packed words},
  author={Vargas, Yannic},
  journal={In preparation},
  year={2022}
}

@article{BGLPV2021,
  title={Hopf algebras of parking functions and decorated planar trees},
  author={Bergeron, Nantel and D'Le{\'o}n, Rafael S Gonz{\'a}lez and Li, Shu Xiao and Pang, CY and Vargas, Yannic},
  journal={arXiv preprint arXiv:2109.05434},
  year={2021}
}


@article{NT2006,
    title = {Polynomial realizations of some trialgebras},
    author = {Novelli, Jean-Christophe and Thibon, Jean-Yves},
    journal = {Formal Power Series and Algebraic Combinatorics},
    year = {2006}
}

@article{Gir2015,
    title = {Combinatorial operads from monoids},
    author = {S. Giraudo},
    journal = {J. Algebr. Comb.},
    volume = {41, Issue 2},
    pages = {493--538},
    year = {2015}
}

@incollection{Hivert2006,
     TITLE = {An introduction to combinatorial {H}opf algebras---examples
              and realizations},
  author={Hivert, Florent},
  booktitle={Physics and theoretical computer science},
  pages={253--274},
  volume = {7},
  year={2006},
  publisher={IOS Press}
}

@article{CG2022,
    author = {Combe, C. and Giraudo, S.},
    title = {{Cliff operads: a hierarchy of operads on words}},
    journal = {J. Algebr. Comb.},
    volume = {57},
        NUMBER = {1},
    pages = {239--269},
    year = {2023},
       DOI = {10.1007/s10801-022-01167-6},
}

@article{Pir2003,
    author = {Pirashvili, T.},
    title = {Sets with two associative operations},
    journal = {Cent. Eur. J. Math.},
    volume = {1},
    year = {2003},
    number = {2},
    pages = {169--183}
}

@article{ZGG2020,
    author = {Zhang, Y. and Gao, X. and Guo, L.},
    title = {{Matching Rota-Baxter algebras, matching dendriform algebras and matching
        pre-Lie algebras}},
    journal = {J. Algebra},
    volume = {552},
    year = {2020},
    pages = {134--170}
}

@misc{oeis,
    Author = {{OEIS Foundation Inc.}},
    URL = { http://oeis.org},
    Title = {The {O}n-{L}ine {E}ncyclopedia of {I}nteger {S}equences},
    Year = 2023}

@article{fresse2017homotopy,
  title={Homotopy of operads and Grothendieck-Teichmuller groups},
  author={Fresse, Benoit},
  year={2017},
  publisher={American Mathematical Soc.}
}

@article{HNT05,
    AUTHOR = {Hivert, F. and Novelli, J.-C. and Thibon, J.-Y.},
     TITLE = {The algebra of binary search trees},
   JOURNAL = {Theoret. Comput. Sci.},
  FJOURNAL = {Theoretical Computer Science},
    VOLUME = {339},
      YEAR = {2005},
    NUMBER = {1},
     PAGES = {129--165}, 
       DOI = {10.1016/j.tcs.2005.01.012}, 
}

@article{KT97,
    AUTHOR = {Krob, Daniel and Thibon, Jean-Yves},
     TITLE = {Noncommutative symmetric functions. {IV}. {Q}uantum linear groups and {H}ecke algebras at {$q=0$}},
   JOURNAL = {J. Algebraic Combin.},
  FJOURNAL = {Journal of Algebraic Combinatorics. An International Journal},
    VOLUME = {6},
      YEAR = {1997},
    NUMBER = {4},
     PAGES = {339--376}, 
       DOI = {10.1023/A:1008673127310}, 
}

@article{Gir12,
    author = {Giraudo, S.},
    title = {{Algebraic and combinatorial structures on pairs of twin binary trees}},
    journal = {J. Algebra},
    volume = {360},
    pages = {115--157},
    year = {2012},
       DOI = {10.1016/j.jalgebra.2012.03.020},
}

@article{DHT02,
    AUTHOR = {Duchamp, G\'{e}rard and Hivert, Florent and Thibon, Jean-Yves},
     TITLE = {Noncommutative symmetric functions. {VI}. {F}ree
              quasi-symmetric functions and related algebras},
   JOURNAL = {Internat. J. Algebra Comput.},
  FJOURNAL = {International Journal of Algebra and Computation},
    VOLUME = {12},
      YEAR = {2002},
    NUMBER = {5},
     PAGES = {671--717}, 
       DOI = {10.1142/S0218196702001139}, 
}

@article{Gir15,
    AUTHOR = {Giraudo, Samuele},
     TITLE = {Combinatorial operads from monoids},
   JOURNAL = {J. Algebraic Combin.},
  FJOURNAL = {Journal of Algebraic Combinatorics. An International Journal},
    VOLUME = {41},
      YEAR = {2015},
    NUMBER = {2},
     PAGES = {493--538}, 
       DOI = {10.1007/s10801-014-0543-4}, 
}

@article{CG22,
    AUTHOR = {Combe, Camille and Giraudo, Samuele},
     TITLE = {Cliff operads: a hierarchy of operads on words},
   JOURNAL = {J. Algebraic Combin.},
  FJOURNAL = {Journal of Algebraic Combinatorics. An International Journal},
    VOLUME = {57},
      YEAR = {2023},
    NUMBER = {1},
     PAGES = {239--269}, 
       DOI = {10.1007/s10801-022-01167-6}, 
}

@article{BF03,
    AUTHOR = {Brouder, Christian and Frabetti, Alessandra},
     TITLE = {Q{ED} {H}opf algebras on planar binary trees},
   JOURNAL = {J. Algebra},
  FJOURNAL = {Journal of Algebra},
    VOLUME = {267},
      YEAR = {2003},
    NUMBER = {1},
     PAGES = {298--322}, 
       DOI = {10.1016/S0021-8693(03)00331-4}, 
}

@article{Lod08,
    author = {Loday, J.-L.},
    title = {{Generalized Bialgebras and Triples of Operads}},
    journal = {Ast{\'e}risque},
    year = {2008},
    volume = {320},
    pages = {1--114}
}

@article{GKLLRT94,
    AUTHOR = {Gelfand, Israel M. and Krob, Daniel and Lascoux, Alain and
              Leclerc, Bernard and Retakh, Vladimir S. and Thibon,
              Jean-Yves},
     TITLE = {Noncommutative symmetric functions},
   JOURNAL = {Adv. Math.},
  FJOURNAL = {Advances in Mathematics},
    VOLUME = {112},
      YEAR = {1995},
    NUMBER = {2},
     PAGES = {218--348}, 
       DOI = {10.1006/aima.1995.1032}, 
}

@phdthesis{Hiv99,
    author = {Hivert, F.},
    title = {{Combinatoire des fonctions quasi-symétriques}},
    school = {Université de Marne la Vallée},
    year = {1999}
}

@article{NT20,
    AUTHOR = {Novelli, Jean-Christophe and Thibon, Jean-Yves},
     TITLE = {Hopf algebras of {$m$}-permutations, {$(m + 1)$}-ary trees,
              and {$m$}-parking functions},
   JOURNAL = {Adv. in Appl. Math.},
  FJOURNAL = {Advances in Applied Mathematics},
    VOLUME = {117},
      YEAR = {2020},
     PAGES = {102019, 55 pp.}, 
       DOI = {10.1016/j.aam.2020.102019}, 
}

@book{LV2012,
    AUTHOR = {Loday, Jean-Louis and Vallette, Bruno},
     TITLE = {Algebraic operads},
    SERIES = {Grundlehren Math. Wiss. [Fundamental
              Principles of Mathematical Sciences]},
    VOLUME = {346},
 PUBLISHER = {Springer, Heidelberg},
      YEAR = {2012},
     PAGES = {xxiv+634 pp.}, 
       DOI = {10.1007/978-3-642-30362-3}, 
}

@article{BGLPV2023,
    AUTHOR = {Bergeron, Nantel and Gonz\'alez D'Le\'on, Rafael S. and Li,
              Shu Xiao and Pang, C. Y. Amy and Vargas, Yannic},
     TITLE = {Hopf algebras of parking functions and decorated planar trees},
   JOURNAL = {Adv. in Appl. Math.},
  FJOURNAL = {Advances in Applied Mathematics},
    VOLUME = {143},
      YEAR = {2023},
     PAGES = {Paper No. 102436, 62 pp.} ,
       DOI = {10.1016/j.aam.2022.102436}, 
}

@book{AM2017,
    AUTHOR = {Aguiar, Marcelo and Mahajan, Swapneel},
     TITLE = {Topics in hyperplane arrangements},
    SERIES = {Mathematical Surveys and Monographs},
    VOLUME = {226},
 PUBLISHER = {American Mathematical Society, {Providence, RI}},
      YEAR = {2017},
     PAGES = {xxiv+611 pp.}, 
       DOI = {10.1090/surv/226}, 
}


@article{McCS2003,
    AUTHOR = {McClure, James E. and Smith, Jeffrey H.},
     TITLE = {Multivariable cochain operations and little {$n$}-cubes},
   JOURNAL = {J. Amer. Math. Soc.},
  FJOURNAL = {Journal of the American Mathematical Society},
    VOLUME = {16},
      YEAR = {2003},
    NUMBER = {3},
     PAGES = {681--704}, 
       DOI = {10.1090/S0894-0347-03-00419-3}, 
}