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

@Misc{Doyle2008,
  author        = {Doyle, P.G. and Rockmore, D.},
  title         = {Riffles, ruffles, and the turning algebra},
  date-added    = {2017-04-25 03:10:34 +0000},
  date-modified = {2017-04-25 03:11:48 +0000},
  eprint        = {0804.0157},
  eprinttype    = {arxiv},
}

@Article{Aguiar2004,
  author        = {Aguiar, M. and Bergeron, N. and Nyman, K.L.},
  title         = {The peak algebra and the descent algebras of types {$B$} and {$D$}},
  journal       = {Trans. Amer. Math. Soc.},
  year          = {2004},
  volume        = {356},
  number        = {7},
  pages         = {2781--2824},
  date-added    = {2017-04-25 03:00:48 +0000},
  date-modified = {2017-04-25 03:00:59 +0000},
  doi           = {10.1090/S0002-9947-04-03541-X},
  fjournal      = {Transactions of the American Mathematical Society},
  mrclass       = {20C30 (05A05 05E15 20F55)},
  mrnumber      = {2052597},
  mrreviewer    = {Christophe Hohlweg},
}

@Article{Loday1989,
  author        = {Loday, J.-L.},
  title         = {Op\'erations sur l'homologie cyclique des alg\`ebres commutatives},
  journal       = {Invent. Math.},
  year          = {1989},
  volume        = {96},
  number        = {1},
  pages         = {205--230},
  doi           = {10.1007/BF01393976},
  fjournal      = {Inventiones Mathematicae},
  mrclass       = {18G35 (19D55)},
  mrnumber      = {981743},
  mrreviewer    = {Sue Geller},
}

@Article{Nyman2003,
  author        = {Nyman, K.L.},
  title         = {The peak algebra of the symmetric group},
  journal       = {J. Algebraic Combin.},
  year          = {2003},
  volume        = {17},
  number        = {3},
  pages         = {309--322},
  doi           = {10.1023/A:1025000905826},
  fjournal      = {Journal of Algebraic Combinatorics. An International Journal},
  mrclass       = {05E05 (05A05 05E10 20C30)},
  mrnumber      = {2001673},
  mrreviewer    = {Marc A. A. van Leeuwen},
}

@Article{Solomon1976,
  author        = {Solomon, L.},
  title         = {A {M}ackey formula in the group ring of a {C}oxeter group},
  journal       = {J. Algebra},
  year          = {1976},
  volume        = {41},
  number        = {2},
  pages         = {255--264},
  doi           = {10.1016/0021-8693(76)90182-4},
}

@article{Adin2001,
	Author = {Adin, Ron M. and Brenti, Francesco and Roichman, Yuval},
	Journal = {Adv. in Appl. Math.},
	Number = {2-3},
	Pages = {210-224},
	Title = {Descent numbers and major indices for the hyperoctahedral group},
	Volume = {27},
	Year = {2001}}

@book{Bona2012,
	Edition = {2nd},
	Publisher = {CRC Press},
	Series = {Discrete Mathematics and its Applications},
	Title = {Combinatorics of {P}ermutations},
	Year = {2012}}

@Article{Braenden2008,
  author    = {Br{\"a}nd{\'e}n, Petter},
  title     = {Actions on permutations and unimodality of descent polynomials},
  journal   = {European J. Combin.},
  year      = {2008},
  volume    = {29},
  number    = {2},
  pages     = {514-531},
}

@article{Carlitz73,
	Author = {Carlitz, L.},
	Fjournal = {Mathematische Nachrichten},
	Journal = {Math. Nachr.},
	Mrclass = {05A15},
	Mrnumber = {0329912 (48 \#8252)},
	Mrreviewer = {D. J. Kleitman},
	Pages = {31--53},
	Title = {Permutations with prescribed pattern},
	Volume = {58},
	Year = {1973}}

@article{Carlitz1976,
	Author = {Carlitz, L. and Scoville, Richard and Vaughan, Theresa},
	Journal = {Manuscripta Math.},
	Number = {3},
	Pages = {211--243},
	Title = {Enumeration of pairs of sequences by rises, falls and levels},
	Volume = {19},
	Year = {1976}}

@article{chebikin,
	Author = {Chebikin, Denis},
	Fjournal = {Electronic Journal of Combinatorics},
	Journal = {Electron. J. Combin.},
	Mrclass = {05A05 (05A10 05A15)},
	Mrnumber = {2448882 (2009g:05003)},
	Mrreviewer = {Toufik Mansour},
	Number = {1},
	Pages = {Research Paper 132, 34 pp.},
	Title = {Variations on descents and inversions in permutations},
	Url = {http://www.combinatorics.org/Volume_15/Abstracts/v15i1r132.html},
	Volume = {15},
	Year = {2008},
	Bdsk-Url-1 = {http://www.combinatorics.org/Volume_15/Abstracts/v15i1r132.html}}

@article{MR675349,
	Author = {Collins, C. B. and Goulden, I. P. and Jackson, D. M. and Nierstrasz, O. M.},
	Coden = {DSMHA4},
	Doi = {10.1016/0012-365X(81)90234-X},
	Fjournal = {Discrete Mathematics},
	Journal = {Discrete Math.},
	Mrclass = {05A15 (15A24)},
	Mrnumber = {675349 (84g:05009)},
	Mrreviewer = {Dominique Foata},
	Number = {2},
	Pages = {139--153},
	Title = {A combinatorial application of matrix {R}iccati equations and their {$q$}-analogue},
	Url = {http://dx.doi.org/10.1016/0012-365X(81)90234-X},
	Volume = {36},
	Year = {1981},
	Bdsk-Url-1 = {http://dx.doi.org/10.1016/0012-365X(81)90234-X}}

@book{David1962,
	Author = {F. N. David and D. E. Barton},
	Publisher = {Lubrecht \& Cramer Ltd},
	Title = {Combinatorial {C}hance},
	Year = {1962}}

@article{Entringer1969,
	Author = {Entringer, R. C.},
	Journal = {Duke Math. J.},
	Pages = {575-579},
	Title = {Enumeration of permutations of $(1,\cdots,n)$ by number of maxima.},
	Volume = {36},
	Year = {1969}}

@book{Flajolet2009,
	Author = {Philippe Flajolet and Robert Sedgewick},
	Owner = {Yan Zhuang},
	Publisher = {Cambridge University Press},
	Timestamp = {2014.07.11},
	Title = {Analytic {C}ombinatorics},
	Year = {2009}}

@article{Foata1978,
	Journal = {Math. Nachr.},
	Owner = {Yan Zhuang},
	Pages = {143-159},
	Timestamp = {2016.09.15},
	Title = {Major index and inversion number of permutations},
	Volume = {83},
	Year = {1978}}

@article{Foata1974,
	Author = {Foata, Dominique and Strehl, Volker},
	Journal = {Math. Z.},
	Owner = {Yan Zhuang},
	Pages = {257-264},
	Timestamp = {2016.08.27},
	Title = {Rearrangements of the symmetric group and enumerative properties of the tangent and secant numbers},
	Volume = {137},
	Year = {1974}}

@article{Froeberg1975,
	Journal = {Math. Scand.},
	Number = {1},
	Owner = {Yan Zhuang},
	Pages = {29-39},
	Timestamp = {2015.02.28},
	Volume = {37},
	Year = {1975}}

@Article{ncsf1,
  author     = {Gelfand, I.M. and Krob, D. and Lascoux, A. and Leclerc, B. and Retakh, V.S. and Thibon, J.-Y.},
  title      = {Noncommutative symmetric functions},
  journal    = {Adv. Math.},
  year       = {1995},
  volume     = {112},
  number     = {2},
  pages      = {218--348},
  coden      = {ADMTA4},
  doi        = {10.1006/aima.1995.1032},
  fjournal   = {Advances in Mathematics},
  mrclass    = {05E05 (15A15 16W30)},
  mrnumber   = {1327096 (96e:05175)},
  mrreviewer = {Arun Ram},
}

@article{Gessel1991,
	Author = {Gessel, Ira M.},
	Journal = {Amer. Math. Monthly},
	Number = {6},
	Owner = {Yan Zhuang},
	Pages = {530--533},
	Timestamp = {2015.02.18},
	Title = {A coloring problem},
	Volume = {98},
	Year = {1991}}

@incollection {Gessel1984,
    AUTHOR = {Gessel, I.M.},
     TITLE = {Multipartite {$P$}-partitions and inner products of skew
              {S}chur functions},
 BOOKTITLE = {Combinatorics and algebra ({B}oulder, {C}olo., 1983)},
    SERIES = {Contemp. Math.},
    VOLUME = {34},
     PAGES = {289--317},
 PUBLISHER = {Amer. Math. Soc., Providence, RI},
      YEAR = {1984},
       DOI = {10.1090/conm/034/777705},
}

@phdthesis{gessel-thesis,
	Author = {Gessel, Ira Martin},
	Mrclass = {Thesis},
	School = {Massachusetts Institute of Technology},
	Title = {Generating {F}unctions and {E}numeration of {S}equences},
	Year = {1977}}

@book{MR2940769x,
	Author = {Gessel, Ira Martin},
	Mrclass = {Thesis},
	Mrnumber = {2940769},
	Note = {Ph.D. Thesis, Massachusetts Institute of Technology},
	Title = {Generating Functions and Enumeration of Sequences},
	Year = {1977}}

@unpublished{greene,
	Author = {Gessel, Ira M. and Greene, Curtis},
	Note = {Unpublished manuscript},
	Owner = {Yan Zhuang},
	Timestamp = {2015.02.18},
	Title = {Permutations with balanced patterns},
	Year = {1990}}

@incollection{Gessel1995,
	Author = {Gessel, Ira M. and Stanley, R.P.},
	Booktitle = {Handbook of Combinatorics, Vol. 2},
	Editor = {R. L. Graham and M. Groetschel and L. Lovasz},
	Owner = {Yan Zhuang},
	Pages = {1021-1061},
	Publisher = {Elsevier},
	Timestamp = {2015.03.30},
	Title = {Algebraic enumeration},
	Year = {1995}}

@Article{Gessel2014,
  author        = {Gessel, I.M. and Zhuang, Y.},
  title         = {Counting permutations by alternating descents},
  journal       = {Electron. J. Combin.},
  year          = {2014},
  volume        = {21},
  number        = {4},
  pages         = {Paper P4.23, 21 pp.},
  date-modified = {2017-04-19 16:07:32 +0000},
  owner         = {Yan Zhuang},
  timestamp     = {2015.02.18},
}

@article{Goulden1985,
	Author = {Goulden, I. P.},
	Journal = {Trans. Amer. Math. Soc.},
	Owner = {Yan Zhuang},
	Pages = {147-160},
	Timestamp = {2017.01.09},
	Title = {A bijective proof of {S}tanley's shuffling theorem},
	Volume = {1},
	Year = {1985}}

@book{MR702512,
	Author = {Goulden, I. P. and Jackson, D. M.},
	Mrclass = {05-02 (05A15)},
	Mrnumber = {702512 (84m:05002)},
	Mrreviewer = {R. W. Robinson},
	Pages = {xxiv+569},
	Publisher = {John Wiley \& Sons, Inc., New York},
	Title = {{C}ombinatorial {E}numeration},
	Year = {1983}}

@article{Goulden1979,
	Author = {Goulden, I. P. and Jackson, D. M.},
	Journal = {J. London Math. Soc. (2)},
	Number = {3},
	Pages = {567-576},
	Title = {An inversion theorem for cluster decompositions of sequences with distinguished subsequences},
	Volume = {20},
	Year = {1979}}

@unpublished{Grinberg2014,
	Author = {Grinberg, Darij and Reiner, Victor},
	Note = {Preprint, \url{https://arxiv.org/abs/1409.8356}},
	Title = {Hopf {A}lgebras in {C}ombinatorics},
	Year = {2014}}

@article{MR0450080,
	Author = {Jackson, D. M. and Aleliunas, R.},
	Fjournal = {Canadian Journal of Mathematics. Journal Canadien de Math\'ematiques},
	Journal = {Canad. J. Math.},
	Mrclass = {05A15},
	Mrnumber = {0450080 (56 \#8379)},
	Mrreviewer = {Michael Henle},
	Number = {5},
	Pages = {971--1009},
	Title = {Decomposition based generating functions for sequences},
	Volume = {29},
	Year = {1977}}

@article{Jacquard1998,
	Author = {Jacquard, Benjamin and Schaeffer, Gilles},
	Journal = {J. Comb. Theory Ser. A},
	Number = {1},
	Pages = {1-20},
	Title = {A bijective census of nonseparable planar maps},
	Volume = {83},
	Year = {1998}}

@book{Kitaev2011,
	Author = {Kitaev, Sergey},
	Publisher = {Springer-Verlag Berlin Heidelberg},
	Title = {Patterns in Permutations and Words},
	Year = {2011}}

@article{Kitaev2007,
	Author = {Kitaev, Sergey},
	Journal = {Discrete Appl. Math.},
	Number = {8},
	Pages = {929-944},
	Title = {Introduction to partially ordered patterns},
	Volume = {115},
	Year = {2007}}

@book{Knuth1973,
	Author = {Knuth, Donald},
	Publisher = {Addison-Wesley Publishing Co.},
	Title = {The Art of Computer Programming},
	Volume = {1: Fundamental Algorithms},
	Year = {1973}}

@article{ncsf2,
	Author = {Krob, D. and Leclerc, B. and Thibon, J.-Y.},
	Doi = {10.1142/S0218196797000113},
	Fjournal = {International Journal of Algebra and Computation},
	Journal = {Internat. J. Algebra Comput.},
	Mrclass = {05E05 (15A15)},
	Mrnumber = {1433196 (98f:05148)},
	Mrreviewer = {Arun Ram},
	Number = {2},
	Pages = {181--264},
	Title = {Noncommutative symmetric functions. {II}. {T}ransformations of alphabets},
	Volume = {7},
	Year = {1997},
}

@article{LaCroix2006,
	Author = {La Croix, Michael},
	Journal = {Discrete Math.},
	Number = {18},
	Pages = {2251-2256},
	Title = {A combinatorial proof of a result of {G}essel and {G}reene},
	Volume = {306},
	Year = {2006}}

@article{Lin2015,
	Author = {Lin, Zhicong and Zeng, Jiang},
	Journal = {J. Comb. Theory Ser. A},
	Pages = {112-129},
	Title = {The $\gamma$-positivity of basic {E}ulerian polynomials via group actions},
	Volume = {135},
	Year = {2015}}

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

@book{macmahon,
	Author = {MacMahon, Percy A.},
	Note = {Originally published in two volumes by Cambridge University Press, 1915--1916},
	Pages = {xix+302+xix+340},
	Publisher = {Chelsea Publishing Co., New York},
	Series = {Two volumes (bound as one)},
	Title = {Combinatory {A}nalysis},
	Year = {1960}}

@unpublished{Mendes,
	Author = {Mendes, Anthony and Remmel, Jeffrey},
	Note = {\rm{Preprint.}},
	Title = {\it{Generating {F}unctions from {S}ymmetric {F}unctions}}}

@Misc{Nicolaescu2012,
  author       = {Liviu Nicolaescu},
  title        = {Combinatorial {M}orse functions and random permutations},
  howpublished = {\url{http://mathoverflow.net/questions/86193}},
  year         = {2012},
}

@article{Noonan1999,
	Author = {Noonan, John and Zeilberger, Doron},
	Journal = {J. Differ. Equations Appl.},
	Number = {4-5},
	Pages = {355-377},
	Title = {The {G}oulden-{J}ackson cluster method: extensions, applications and implementations},
	Volume = {5},
	Year = {1999}}

@incollection{Odlyzko1995,
	Author = {A. M. Odlyzko},
	Booktitle = {Handbook of Combinatorics, Vol. 2},
	Editor = {R. L. Graham and M. Groetschel and L. Lovasz},
	Pages = {1063-1229},
	Publisher = {Elsevier},
	Title = {Asymptotic enumeration methods},
	Year = {1995}}

@Book{Petersen2015,
  title     = {Eulerian Numbers},
  publisher = {Birkh\"auser/Springer, New York},
  year      = {2015},
  author    = {Petersen, T.K.},
}

@article{Petersen2013,
	Author = {Petersen, T.K.},
	Journal = {Math. Mag.},
	Number = {3},
	Pages = {159-176},
	Title = {Two-sided {E}ulerian polynomials via balls in boxes},
	Volume = {86},
	Year = {2013}}

@Article{Petersen2007,
  author    = {Petersen, T.K.},
  title     = {Enriched ${P}$-partitions and peak algebras},
  journal   = {Adv. Math.},
  year      = {2007},
  volume    = {209},
  number    = {2},
  pages     = {561-610},
  DOI = {10.1016/j.aim.2006.05.016}
}

@phdthesis{Petersen2006,
	Author = {Petersen, T. Kyle},
	School = {Brandeis University},
	Title = {Descents, {P}eaks, and ${P}$-partitions},
	Year = {2006}}

@article{remmel,
	Author = {Remmel, Jeffrey B.},
	Doi = {10.1007/s00026-012-0150-9},
	Fjournal = {Annals of Combinatorics},
	Journal = {Ann. Comb.},
	Mrclass = {05A05 (05A15 05E05)},
	Mrnumber = {2960023},
	Mrreviewer = {Eric S. Egge},
	Number = {3},
	Pages = {625--650},
	Title = {Generating functions for alternating descents and alternating major index},
	Volume = {16},
	Year = {2012}
}

@Article{Shapiro1983,
  author    = {Shapiro, Louis W. and Woan, Wen-Jin and Getu, Seyoum},
  title     = {Runs, slides, and moments},
  journal   = {SIAM J. Alg. Disc. Meth.},
  year      = {1983},
  volume    = {4},
  number    = {4},
  pages     = {459-466},
}

@misc{oeis,
	Author = {N. J. A. Sloane},
	Note = {Published electronically at \url{http://oeis.org}, 2015},
	Title = {The {O}n-{L}ine {E}ncyclopedia of {I}nteger {S}equences}}

@article{Stadler1999,
	Author = {Stadler, Jonathan D.},
	Journal = {J. Comb. Theory Ser. A},
	Number = {1},
	Pages = {176-187},
	Title = {Stanley's shuffling theorem revisited},
	Volume = {88},
	Year = {1999}}

@Book{Stanley1972,
  title         = {Ordered {S}tructures and {P}artitions},
  publisher     = {American Mathematical Society},
  year          = {1972},
  author        = {Stanley, R.P.},
  volume        = {119},
  series        = {Memoirs of the American Mathematical Society},
  PAGES         = {iii+104}
}

@Book{Stanley2011,
  title         = {Enumerative {C}ombinatorics, Vol. 1},
  publisher     = {Cambridge University Press},
  year          = {2012},
  author        = {Stanley, R.P.},
  edition       = {2nd Edition},
  SERIES = {Cambridge Studies in Advanced Mathematics},
  PAGES = {xiv+626}
}

@Book{Stanley2001,
  title         = {Enumerative {C}ombinatorics, Vol. 2},
  publisher     = {Cambridge University Press},
  year          = {{\noopsort{b}}2001},
  author        = {Stanley, R.P.},
}

@incollection{st-alt,
	Author = {Stanley, R.P.},
	Booktitle = {Combinatorics and graphs},
	Doi = {10.1090/conm/531/10466},
	Mrclass = {05-02 (05A05 05E05 05E10)},
	Mrnumber = {2757798 (2012d:05015)},
	Mrreviewer = {Domenico Senato},
	Pages = {165--196},
	Publisher = {Amer. Math. Soc., Providence, RI},
	Series = {Contemp. Math.},
	Title = {A survey of alternating permutations},
	Volume = {531},
	Year = {2010}
}

@article{Stanley2008,
	Author = {Stanley, Richard P.},
	Journal = {Michigan Math. J.},
	Pages = {675-687},
	Title = {Longest alternating subsequences of permutations},
	Volume = {57},
	Year = {2008}}

@article{Stanley1976,
	Author = {Stanley, Richard P.},
	Journal = {J. Comb. Theory},
	Pages = {336-356},
	Title = {Binomial posets, {M}\"obius inversion, and permutation enumeration},
	Volume = {20},
	Year = {1976}}


@article{Steingrimsson1994,
	Journal = {European J. Combin.},
	Number = {2},
	Pages = {187-205},
	Title = {Permutation statistics of indexed permutations},
	Volume = {15},
	Year = {1994}}

@Article{Stembridge1997,
  author    = {Stembridge, J.R.},
  title     = {Enriched ${P}$-partitions},
  journal   = {Trans. Amer. Math. Soc.},
  year      = {1997},
  volume    = {349},
  number    = {2},
  pages     = {763-788},
  DOI = {10.1090/S0002-9947-97-01804-7}
}

@article{Stump2009,
	Author = {Stump, Christian},
	Pages = {Article B60a, 17},
	Title = {On bijections between 231-avoiding permutations and {D}yck paths},
	Volume = {60},
	Year = {2009}}

@inproceedings{Vong2013,
	Author = {Vong, Vincent},
	Booktitle = {25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013)},
	Pages = {813--824},
	Series = {Discrete Math. Theor. Compt. Sci. Proc.},
	Title = {Algebraic properties of some permutation statistics},
	Year = {2013}}

@phdthesis{West1990,
	Author = {West, Julian},
	School = {Massachusetts Institute of Technology},
	Title = {Permutations with forbidden subsequences and stack-sortable permutations},
	Year = {1990}}

@article{Zhuang2016,
	Author = {Zhuang, Yan},
	Journal = {J. Comb. Theory Ser. A},
	Pages = {147-176},
	Title = {Counting permutations by runs},
	Volume = {142},
	Year = {2016}}

@Article{Zhuang2017,
  author    = {Zhuang, Yan},
  title     = {Eulerian polynomials and descent statistics},
  journal   = {Adv. in Appl. Math.},
  year      = {2017},
  volume    = {90},
  pages     = {86-144},
}

@phdthesis{Chow2001,
	Author = {Chow, Chak-On},
	School = {Massachusetts Institute of Technology},
	Title = {Noncommutative symmetric functions of type {B}},
	Year = {2001}}

@Article{Gessel2017,
  author = {Gessel, I.M. and Zhuang, Y.},
  title  = {Shuffle-compatible permutation statistics},
  journal = {Adv. Math.},
  volume = {332},
  pages = {85--141},
  year = {2018},
  doi = {10.1016/j.aim.2018.05.003}
}

@Unpublished{Zhuang2015,
  author = {Zhuang, Yan},
  title  = {A generalized {G}oulden--{J}ackson cluster method and lattice path enumeration},
  note   = {To appear in \emph{Discrete Math.}},
}

@Unpublished{Lin2016,
  author = {Lin, Zhicong and Kim, Dongsu},
  title  = {A sextuple equidistribution arising in pattern avoidance},
  note   = {Preprint, \url{https://arxiv.org/abs/1612.02964}.},
  year   = {2016},
}

@Article{Malvenuto1995,
  author  = {Malvenuto, Clauda and Reutenauer, Christophe},
  title   = {Duality between quasi-symmetric functions and the {S}olomon descent algebra},
  journal = {J. Algebra},
  year    = {1995},
  volume  = {177},
  number  = {3},
  pages   = {967--982},
}

@Article{Simion1985,
  author  = {Simion, Rodica and Schmidt, Frank W.},
  title   = {Restricted permutations},
  journal = {European J. Combin.},
  year    = {1985},
  volume  = {6},
  number  = {4},
  pages   = {383--406},
}

@Article{Elizalde2003,
  author  = {Elizalde, Sergi and Noy, Marc},
  title   = {Consecutive patterns in permutations},
  journal = {Adv. in Appl. Math.},
  year    = {2003},
  volume  = {30},
  number  = {1-2},
  pages   = {110--125},
}

@Article{Elizalde2012,
  author  = {Elizalde, Sergi and Noy, Marc},
  title   = {Clusters, generating functions and asymptotics for consecutive patterns in permutations},
  journal = {Adv. in Appl. Math.},
  year    = {2012},
  volume  = {49},
  number  = {3-5},
  pages   = {351--374},
}

@Article{Rawlings2007,
  author  = {Rawlings, Don},
  title   = {The {$q$}-exponential generating function for permutations by consecutive patterns and inversions},
  journal = {J. Combin. Theory Ser. A},
  year    = {2007},
  volume  = {114},
  number  = {1},
  pages   = {184--193},
}

@Article{Carlitz1966,
  author  = {Carlitz, L. and Roselle, D. P. and Scoville, R. A.},
  title   = {Permutations and sequences with repetitions by number of increases},
  journal = {J. Combinatorial Theory},
  year    = {1966},
  volume  = {1},
  pages   = {350--374},
}

@Article{Aguiar2006,
  author  = {Aguiar, M. and Bergeron, N. and Sottile, F.},
  title   = {Combinatorial {H}opf algebras and generalized {D}ehn-{S}ommerville relations},
  journal = {Compos. Math.},
  year    = {2006},
  volume  = {142},
  number  = {1},
  pages   = {1--30},
  URL = {https://doi.org/10.1112/S0010437X0500165X}
}

@Article{Hsiao2010,
  author   = {Hsiao, Samuel K. and Petersen, T. Kyle},
  title    = {Colored posets and colored quasisymmetric functions},
  journal  = {Ann. Comb.},
  year     = {2010},
  volume   = {14},
  number   = {2},
  pages    = {251--289},
  fjournal = {Annals of Combinatorics},
}

@Article{Baumann2008,
  author  = {Baumann, Pierre and Hohlweg, Christophe},
  title   = {A {S}olomon descent theory for the wreath products {$G\wr \mathfrak{S}_n$}},
  journal = {Trans. Amer. Math. Soc.},
  year    = {2008},
  volume  = {360},
  number  = {3},
  pages   = {1475--1538},
}

@Article{Novelli2010,
  author  = {Novelli, Jean-Christophe and Thibon, Jean-Yves},
  title   = {Free quasi-symmetric functions and descent algebras for wreath products, and noncommutative multi-symmetric functions},
  journal = {Discrete Math.},
  year    = {2010},
  volume  = {310},
  number  = {24},
  pages   = {3584--3606},
}

@Article{Mantaci1995,
  author  = {Mantaci, R. and Reutenauer, C.},
  title   = {A generalization of {S}olomon's algebra for hyperoctahedral groups and other wreath products},
  journal = {Comm. Algebra},
  year    = {1995},
  volume  = {23},
  number  = {1},
  pages   = {27--56},
}

@Article{Bergeron2006,
  author  = {Bergeron, Nantel and Hohlweg, Christophe},
  title   = {Coloured peak algebras and {H}opf algebras},
  journal = {J. Algebraic Combin.},
  year    = {2006},
  volume  = {24},
  number  = {3},
  pages   = {299--330},
}

@Article{Grinberg2017a,
  author  = {Grinberg, D.},
  title   = {Dual creation operators and a dendriform algebra structure on the quasisymmetric functions},
  journal = {Canad. J. Math.},
  year    = {2017},
  volume  = {69},
  number  = {1},
  pages   = {21--53},
  DOI = {10.4153/CJM-2016-018-8}
}

@Article{Schocker2005,
  author  = {Schocker, M.},
  title   = {The peak algebra of the symmetric group revisited},
  journal = {Adv. Math.},
  year    = {2005},
  volume  = {192},
  number  = {2},
  pages   = {259--309},
  DOI = {10.1016/j.aim.2004.04.007}
}

@Article{Dokos2012,
  author  = {Dokos, Theodore and Dwyer, Tim and Johnson, Bryan P. and Sagan, Bruce E. and Selsor, Kimberly},
  title   = {Permutation patterns and statistics},
  journal = {Discrete Math.},
  year    = {2012},
  volume  = {312},
  number  = {18},
  pages   = {2760--2775},
}

@misc{Grinberg2017,
  author = {Grinberg, D.},
  title  = {Shuffle-compatible permutation statistics {II}: {T}he exterior peak set},
  eprinttype = {arxiv},
  eprint = {1806.04114},
}

@Article{Josuat-Verges2016,
  author        = {Josuat-Verg\`es, M. and Pang, C.Y.A.},
  title         = {Subalgebras of {S}olomon's descent algebra based on alternating runs},
  journal       = {J. Combin. Theory Ser. A},
  year          = {2018},
  volume        = {158},
  pages         = {36--65},
  DOI = {10.1016/j.jcta.2018.03.012}
}

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