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@misc{amrsa,
    AUTHOR = {amrsa},
     TITLE = {Why an alternative magma need not even be power\hyp{}associative?},
 PUBLISHER = {Mathematics Stack Exchange}, 
       URL = {https://math.stackexchange.com/q/3132319},
      Note = {version: 2019-03-01},
}

@book{Bergman,
    AUTHOR = {Bergman, Clifford},
     TITLE = {Universal algebra},
    SERIES = {Pure and Applied Mathematics (Boca Raton)},
    VOLUME = {301},
      NOTE = {Fundamentals and selected topics},
 PUBLISHER = {CRC Press, Boca Raton, FL},
      YEAR = {2012},
     PAGES = {xii+308},
      ISBN = {978-1-4398-5129-6},
   MRCLASS = {08-02 (06-02 08A40 08B05 08B10 08B26)},
  MRNUMBER = {2839398},
MRREVIEWER = {Konrad P. Pi\'{o}ro},
}


@article{Birkhoff,
AUTHOR = {Birkhoff, G.},
     TITLE = {On the structure of abstract algebras},
   JOURNAL = {Proc. Cambr. Philos. Soc.},
  FJOURNAL = {Proceedings of the Cambridge Philosophical Society},
    VOLUME = {31},
      YEAR = {1935},
     PAGES = {433--454},
}

@article {Subassociative,
    AUTHOR = {Braitt, Milton S. and Silberger, Donald},
     TITLE = {Subassociative groupoids},
   JOURNAL = {Quasigroups Related Systems},
  FJOURNAL = {Quasigroups and Related Systems},
    VOLUME = {14},
      YEAR = {2006},
    NUMBER = {1},
     PAGES = {11--26},
      ISSN = {1561-2848},
   MRCLASS = {20N02 (05A15)},
  MRNUMBER = {2268823},
}

@incollection {AssociativeSpectra1,
    AUTHOR = {Cs\'{a}k\'{a}ny, B\'{e}la and Waldhauser, Tam\'{a}s},
     TITLE = {Associative spectra of binary operations},
      NOTE = {Ivo G. Rosenberg's 65th birthday},
   JOURNAL = {Mult.-Valued Log.},
  FJOURNAL = {Multiple-Valued Logic. An International Journal},
    VOLUME = {5},
      YEAR = {2000},
    NUMBER = {3},
     PAGES = {175--200},
      ISSN = {1023-6627},
   MRCLASS = {20N02},
  MRNUMBER = {1784270},
}

@article {EvenLempel,
    AUTHOR = {Even, Shimon and Lempel, Abraham},
     TITLE = {Generation and enumeration of all solutions of the
              characteristic sum condition},
   JOURNAL = {Information and Control},
  FJOURNAL = {Information and Control},
    VOLUME = {21},
      YEAR = {1972},
     PAGES = {476--482},
      ISSN = {0019-9958},
   MRCLASS = {94A10},
  MRNUMBER = {349273},
MRREVIEWER = {C. F. Picard},
}

@article {CatMod,
    AUTHOR = {Hein, Nickolas and Huang, Jia},
     TITLE = {Modular {C}atalan numbers},
   JOURNAL = {European J. Combin.},
  FJOURNAL = {European Journal of Combinatorics},
    VOLUME = {61},
      YEAR = {2017},
     PAGES = {197--218},
      ISSN = {0195-6698},
   MRCLASS = {05A19 (05A10)},
  MRNUMBER = {3588717},
MRREVIEWER = {David Callan},
       DOI = {10.1016/j.ejc.2016.11.004},
       URL = {https://doi.org/10.1016/j.ejc.2016.11.004},
}

@article {VarCat,
    AUTHOR = {Hein, Nickolas and Huang, Jia},
     TITLE = {Variations of the {C}atalan numbers from some nonassociative
              binary operations},
   JOURNAL = {Discrete Math.},
  FJOURNAL = {Discrete Mathematics},
    VOLUME = {345},
      YEAR = {2022},
    NUMBER = {3},
     PAGES = {Paper No. 112711, 18},
      ISSN = {0012-365X},
   MRCLASS = {05A19 (05A10)},
  MRNUMBER = {4340747},
       DOI = {10.1016/j.disc.2021.112711},
       URL = {https://doi.org/10.1016/j.disc.2021.112711},
}

@article {Hamming,
    AUTHOR = {Huang, Jia},
     TITLE = {Norton algebras of the {H}amming graphs via linear characters},
   JOURNAL = {Electron. J. Combin.},
  FJOURNAL = {Electronic Journal of Combinatorics},
    VOLUME = {28},
      YEAR = {2021},
    NUMBER = {2},
     PAGES = {Paper No. 2.30, 36},
   MRCLASS = {05E30 (05A15 17D99)},
  MRNUMBER = {4272719},
MRREVIEWER = {Sung-Yell Song},
       DOI = {10.37236/10251},
       URL = {https://doi.org/10.37236/10251},
}

@article {DoubleMinus,
    AUTHOR = {Huang, Jia and Mickey, Madison and Xu, Jianbai},
     TITLE = {The nonassociativity of the double minus operation},
   JOURNAL = {J. Integer Seq.},
  FJOURNAL = {Journal of Integer Sequences},
    VOLUME = {20},
      YEAR = {2017},
    NUMBER = {10},
     PAGES = {Art. 17.10.3, 11},
   MRCLASS = {05A15},
  MRNUMBER = {3745202},
MRREVIEWER = {Philip B. Zhang},
}

@article {GM,
    AUTHOR = {Giorgilli, A. and Molteni, G.},
     TITLE = {Representation of a 2-power as sum of {$k$} 2-powers: a
              recursive formula},
   JOURNAL = {J. Number Theory},
  FJOURNAL = {Journal of Number Theory},
    VOLUME = {133},
      YEAR = {2013},
    NUMBER = {4},
     PAGES = {1251--1261},
      ISSN = {0022-314X},
   MRCLASS = {11A67 (11B65)},
  MRNUMBER = {3003997},
MRREVIEWER = {Vilius Stakenas},
       DOI = {10.1016/j.jnt.2012.09.013},
       URL = {https://doi.org/10.1016/j.jnt.2012.09.013},
}

@misc{Knuth,
    AUTHOR = {Knuth, D. E.},
     TITLE = {Letter to R. E. Tarjan and N. J. A. Sloane},
     MONTH = {July},
      YEAR = {1975}, 
       URL = {https://oeis.org/A007178/a007178.pdf},
}

@article {KrennWagner,
    AUTHOR = {Krenn, Daniel and Wagner, Stephan},
     TITLE = {Compositions into powers of {$b$}: asymptotic enumeration and
              parameters},
   JOURNAL = {Algorithmica},
  FJOURNAL = {Algorithmica. An International Journal in Computer Science},
    VOLUME = {75},
      YEAR = {2016},
    NUMBER = {4},
     PAGES = {606--631},
      ISSN = {0178-4617},
   MRCLASS = {11B75 (11P70)},
  MRNUMBER = {3509386},
MRREVIEWER = {Weidong Gao},
       DOI = {10.1007/s00453-015-0061-3},
       URL = {https://doi.org/10.1007/s00453-015-0061-3},
}

@article {LST,
    AUTHOR = {Lehr, Siegfried and Shallit, Jeffrey and Tromp, John},
     TITLE = {On the vector space of the automatic reals},
   JOURNAL = {Theoret. Comput. Sci.},
  FJOURNAL = {Theoretical Computer Science},
    VOLUME = {163},
      YEAR = {1996},
    NUMBER = {1-2},
     PAGES = {193--210},
      ISSN = {0304-3975},
   MRCLASS = {03F60},
  MRNUMBER = {1407021},
MRREVIEWER = {Cristian Calude},
       DOI = {10.1016/0304-3975(95)00234-0},
       URL = {https://doi.org/10.1016/0304-3975(95)00234-0},
}

@article {GraphAlgebra1,
    AUTHOR = {Lehtonen, Erkko and Waldhauser, Tam\'{a}s},
     TITLE = {Associative spectra of graph algebras {I}. {F}oundations,
              undirected graphs, antiassociative graphs},
   JOURNAL = {J. Algebraic Combin.},
  FJOURNAL = {Journal of Algebraic Combinatorics. An International Journal},
    VOLUME = {53},
      YEAR = {2021},
    NUMBER = {3},
     PAGES = {613--638},
      ISSN = {0925-9899},
   MRCLASS = {05C25 (03C05 05C20 20N02)},
  MRNUMBER = {4258061},
MRREVIEWER = {Michael Kompatscher},
       DOI = {10.1007/s10801-020-01010-w},
       URL = {https://doi.org/10.1007/s10801-020-01010-w},
}

@article {GraphAlgebra2,
    AUTHOR = {Lehtonen, Erkko and Waldhauser, Tam\'{a}s},
     TITLE = {Associative spectra of graph algebras {II}: satisfaction of
              bracketing identities, spectrum dichotomy},
   JOURNAL = {J. Algebraic Combin.},
  FJOURNAL = {Journal of Algebraic Combinatorics. An International Journal},
    VOLUME = {55},
      YEAR = {2022},
    NUMBER = {2},
     PAGES = {533--557},
      ISSN = {0925-9899},
   MRCLASS = {05C25 (03C05 05C20 20N02)},
  MRNUMBER = {4390596},
MRREVIEWER = {Michael Kompatscher},
       DOI = {10.1007/s10801-021-01061-7},
       URL = {https://doi.org/10.1007/s10801-021-01061-7},
}

@article {AssociativeSpectra2,
    AUTHOR = {Liebscher, Sebastian and Waldhauser, Tam\'{a}s},
     TITLE = {On associative spectra of operations},
   JOURNAL = {Acta Sci. Math. (Szeged)},
  FJOURNAL = {Acta Universitatis Szegediensis. Acta Scientiarum
              Mathematicarum},
    VOLUME = {75},
      YEAR = {2009},
    NUMBER = {3-4},
     PAGES = {433--456},
      ISSN = {0001-6969},
   MRCLASS = {08B05 (08A62 08B15)},
  MRNUMBER = {2590342},
MRREVIEWER = {James B. Nation},
}

@book {Operads,
    AUTHOR = {Loday, Jean-Louis and Vallette, Bruno},
     TITLE = {Algebraic operads},
    SERIES = {Grundlehren der mathematischen Wissenschaften [Fundamental
              Principles of Mathematical Sciences]},
    VOLUME = {346},
 PUBLISHER = {Springer, Heidelberg},
      YEAR = {2012},
     PAGES = {xxiv+634},
      ISBN = {978-3-642-30361-6},
   MRCLASS = {18D50 (16E99)},
  MRNUMBER = {2954392},
MRREVIEWER = {Andrey Yu. Lazarev},
       DOI = {10.1007/978-3-642-30362-3},
       URL = {https://doi.org/10.1007/978-3-642-30362-3},
}

@misc{OEIS,
  author={Sloane, Neil J. A. and The OEIS Foundation Inc.},
  title={The on-line encyclopedia of integer sequences},
  year={2020},
  url={http://oeis.org/?language=english},
}

@article {Schafer,
    AUTHOR = {Schafer, R. D.},
     TITLE = {On the algebras formed by the {C}ayley-{D}ickson process},
   JOURNAL = {Amer. J. Math.},
  FJOURNAL = {American Journal of Mathematics},
    VOLUME = {76},
      YEAR = {1954},
     PAGES = {435--446},
      ISSN = {0002-9327},
   MRCLASS = {09.1X},
  MRNUMBER = {61098},
MRREVIEWER = {I. M. H. Etherington},
       DOI = {10.2307/2372583},
       URL = {https://doi.org/10.2307/2372583},
}

@book {EC2,
    AUTHOR = {Stanley, Richard P.},
     TITLE = {Enumerative combinatorics. {V}ol. 2},
    SERIES = {Cambridge Studies in Advanced Mathematics},
    VOLUME = {62},
      NOTE = {With a foreword by Gian-Carlo Rota and appendix 1 by Sergey
              Fomin},
 PUBLISHER = {Cambridge University Press, Cambridge},
      YEAR = {1999},
     PAGES = {xii+581},
      ISBN = {0-521-56069-1; 0-521-78987-7},
   MRCLASS = {05A15 (05-02 05E05 05E10 68R05)},
  MRNUMBER = {1676282},
MRREVIEWER = {Ira Gessel},
       DOI = {10.1017/CBO9780511609589},
       URL = {https://doi.org/10.1017/CBO9780511609589},
}

@article {Takacs,
    AUTHOR = {Tak\'{a}cs, Lajos},
     TITLE = {Enumeration of rooted trees and forests},
   JOURNAL = {Math. Sci.},
  FJOURNAL = {The Mathematical Scientist},
    VOLUME = {18},
      YEAR = {1993},
    NUMBER = {1},
     PAGES = {1--10},
      ISSN = {0312-3685},
   MRCLASS = {05C05 (05C30)},
  MRNUMBER = {1227236},
MRREVIEWER = {J. W. Moon},
}