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@Preamble{"\providecommand\noopsort[1]{}"}

 @article {Adin2021,
    AUTHOR = {Adin, Ron M. and Gessel, Ira M. and Reiner, Victor and Roichman, Yuval},
     TITLE = {Cyclic quasi-symmetric functions},
   JOURNAL = {Israel J. Math.},
  FJOURNAL = {Israel Journal of Mathematics},
    VOLUME = {243},
      YEAR = {2021},
    NUMBER = {1},
     PAGES = {437--500}
}

@Article{Detal:csc,
  author     = {Domagalski, Rachel and Liang, Jinting and Minnich, Quinn and Sagan, Bruce E. and Schmidt, Jamie and Sietsema, Alexander},
  journal    = {S\'{e}m. Lothar. Combin.},
  title      = {Cyclic shuffle compatibility},
  year       = {[2020--2021]},
  pages      = {Art. B85d, 11 pp.},
  volume     = {85},
  fjournal   = {S\'{e}minaire Lotharingien de Combinatoire},
  mrclass    = {05A05 (05A19)},
  mrnumber   = {4329764},
  mrreviewer = {David Callan},
}

@article {Gessel2018,
    AUTHOR = {Gessel, Ira M. and Zhuang, Yan},
     TITLE = {Shuffle-compatible permutation statistics},
   JOURNAL = {Adv. Math.},
  FJOURNAL = {Advances in Mathematics},
    VOLUME = {332},
      YEAR = {2018},
     PAGES = {85--141}
}

@book {sag:aoc,
    AUTHOR = {Sagan, Bruce E.},
     TITLE = {Combinatorics: the art of counting},
    SERIES = {Graduate Studies in Mathematics},
    VOLUME = {210},
 PUBLISHER = {American Mathematical Society, Providence, RI},
      YEAR = {[2020] \copyright 2020},
     PAGES = {xix+304},
      ISBN = {978-1-4704-6032-7},
   MRCLASS = {05-01 (05Axx 05Exx 06-01)},
  MRNUMBER = {4249619},
MRREVIEWER = {Ulrich Tamm},
}

@book {sta:osp,
    AUTHOR = {Stanley, Richard P.},
     TITLE = {Ordered structures and partitions},
    SERIES = {Memoirs of the American Mathematical Society, No. 119},
 PUBLISHER = {American Mathematical Society, Providence, R.I.},
      YEAR = {1972},
     PAGES = {iii+104},
   MRCLASS = {05A17},
  MRNUMBER = {0332509},
MRREVIEWER = {L. K. Durst},
}

@misc{2209.00051,
  author = {Jinting Liang},
  eprint   = {2209.00051},
  title  = {Enriched toric $[\vec{D}]$-partitions},
  year   = {2022},
}

@article{Stembridge1997,
	Author = {Stembridge, John R.},
	Journal = {Trans. Amer. Math. Soc.},
	Number = {2},
	Owner = {Yan Zhuang},
	Pages = {763-788},
	Timestamp = {2016.08.20},
	Title = {Enriched ${P}$-partitions},
	Volume = {349},
	Year = {1997}}

@Article{BakerJarvis2020,
  author  = {Baker-Jarvis, Duff and Sagan, Bruce E.},
  journal = {Adv. in Appl. Math.},
  title   = {Bijective proofs of shuffle compatibility results},
  year    = {2020},
  issn    = {0196-8858},
  pages   = {101973, 29},
  volume  = {113},
}

@Article{Yang2022,
  author  = {Yang, Lihong and Yan, Sherry H. F.},
  journal = {Electron. J. Combin.},
  title   = {On a conjecture concerning shuffle-compatible permutation statistics},
  year    = {2022},
  number  = {3},
  pages   = {Paper No. 3.3, 11 pp.},
  volume  = {29},
}

@Article{Grinberg2018,
  author  = {Grinberg, Darij},
  journal = {Electron. J. Combin.},
  title   = {Shuffle-compatible permutation statistics {II}: the exterior peak set},
  year    = {2018},
  number  = {4},
  pages   = {Paper No. 4.17, 61 pp.},
  volume  = {25},
}

@Unpublished{Zhuang2021,
  author = {Zhuang, Yan},
  note   = {To appear in \textit{Algebr. Comb.}},
  title  = {A lifting of the {G}oulden--{J}ackson cluster method to the {M}alvenuto--{R}eutenauer algebra},
  year   = {2022},
}


@book{Stanley2011,
	Author = {Stanley, Richard P.},
	Date-Modified = {2017-04-19 16:14:09 +0000},
	Edition = {2nd},
	Owner = {Yan Zhuang},
	Publisher = {Cambridge University Press},
	Timestamp = {2014.07.08},
	Title = {Enumerative {C}ombinatorics, Vol. 1},
	Year = {{\noopsort{a}}2011}}

@book{Stanley2001,
	Author = {Stanley, Richard P.},
	Date-Modified = {2017-04-19 16:24:21 +0000},
	Owner = {Yan Zhuang},
	Publisher = {Cambridge University Press},
	Timestamp = {2014.07.08},
	Title = {Enumerative {C}ombinatorics, Vol. 2},
	Year = {{\noopsort{b}}2001}}

@Article{KantarciOguz2018,
  author  = {Kantarc{\i} O\u{g}uz, Ezgi},
  journal = {Electron. J. Combin.},
  title   = {A Counterexample to the Shuffle Compatibility Conjecture},
  year    = {2022},
  number  = {3},
  pages   = {Paper No. 3.51, 5 pp.},
  volume  = {29},
}

@misc{Ji2022,
  author = {Ji, Kathy Q. and Zhang, Dax T. X.},
  eprint   = {2205.03188},
  title  = {A cyclic analogue of {S}tanley's shuffling theorem},
  year   = {2022},
}

@article{Gessel1984,
	Author = {Gessel, Ira M.},
	Journal = {Contemp. Math.},
	Owner = {Yan Zhuang},
	Pages = {289--317},
	Timestamp = {2017.02.09},
	Title = {Multipartite {$P$}-partitions and inner products of skew {S}chur functions},
	Volume = {34},
	Year = {1984}}

@Unpublished{Grinberg2020,
  author        = {Grinberg, Darij and Reiner, Victor},
  note          = {Preprint, \url{https://arxiv.org/abs/1409.8356v7}},
  title         = {Hopf {A}lgebras in {C}ombinatorics},
  year          = {2020},
  date-modified = {2017-04-25 02:31:27 +0000},
  owner         = {Yan Zhuang},
  timestamp     = {2017.01.10},
}

@book{Luoto2013,
	Author = {Luoto, Kurt and Mykytiuk, Stefan and van Willigenburg, Stephanie},
	Owner = {Yan Zhuang},
	Publisher = {Springer},
	Timestamp = {2017.02.09},
	Title = {{An Introduction to Quasisymmetric Schur Functions. Hopf Algebras, Quasisymmetric Functions, and Young Composition Tableaux.}},
	Year = {2013}}

@PhdThesis{Moustakas2022,
  author = {Moustakas, Vasileios Dionysios},
  school = {National and Kapodistrian University of Athens},
  title  = {Enumerative combinatorics, representations and quasisymmetric functions},
  year   = {2022},
}

@Book{macmahon,
  title     = {Combinatory {A}nalysis},
  publisher = {Chelsea Publishing Co., New York},
  year      = {1960},
  author    = {MacMahon, P. A.},
  series    = {Two volumes (bound as one)},
  note      = {Originally published in two volumes by Cambridge University Press, 1915--1916},
  pages     = {xix+302+xix+340},
}

@misc{LSZ,
  author = {Liang, Jinting and Sagan, Bruce E. and Zhuang, Yan},
  eprint   = {2212.14522},
  title  = {Cyclic shuffle-compatibility via cyclic shuffle algebras},
  year	 = {2023},
}

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