@article {Bayer-Billera,
    AUTHOR = {Bayer, Margaret M. and Billera, Louis J.},
     TITLE = {Generalized {D}ehn-{S}ommerville relations for polytopes,
              spheres and {E}ulerian partially ordered sets},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {79},
      YEAR = {1985},
    NUMBER = {1},
     PAGES = {143--157},
      ISSN = {0020-9910},
   MRCLASS = {52A25 (05A15 06A10)},
  MRNUMBER = {774533},
MRREVIEWER = {P. McMullen},
       DOI = {10.1007/BF01388660},
       opturl = {https://doi.org/10.1007/BF01388660},
}

@article{Bayer-Klapper,
    AUTHOR = {Bayer, Margaret M. and Klapper, Andrew},
     TITLE = {A new index for polytopes},
   JOURNAL = {Discrete Comput. Geom.},
  FJOURNAL = {Discrete \& Computational Geometry. An International Journal
              of Mathematics and Computer Science},
    VOLUME = {6},
      YEAR = {1991},
    NUMBER = {1},
     PAGES = {33--47},
      ISSN = {0179-5376},
   MRCLASS = {52B40 (52B11)},
  MRNUMBER = {1073071},
MRREVIEWER = {P. McMullen},
       DOI = {10.1007/BF02574672},
       opturl = {https://doi.org/10.1007/BF02574672},
}
  
@book{Doker,
    AUTHOR = {Doker, Jeffrey Samuel},
     TITLE = {Geometry of {G}eneralized {P}ermutohedra},
      NOTE = {Thesis (Ph.D.)--University of California, Berkeley},
 PUBLISHER = {ProQuest LLC, Ann Arbor, MI},
      YEAR = {2011},
     PAGES = {74},
      ISBN = {978-1267-22787-4},
   MRCLASS = {Thesis},
  MRNUMBER = {3022511},
       URL = {http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqm&rft_dat=xri:pqdiss:3498957},
}
  
@article {Ehrenborg-Readdy,
    AUTHOR = {Ehrenborg, Richard and Readdy, Margaret},
     TITLE = {The {T}chebyshev transforms of the first and second kind},
   JOURNAL = {Ann. Comb.},
  FJOURNAL = {Annals of Combinatorics},
    VOLUME = {14},
      YEAR = {2010},
    NUMBER = {2},
     PAGES = {211--244},
      ISSN = {0218-0006},
   MRCLASS = {05E15 (06A11 16T30)},
  MRNUMBER = {2653890},
       DOI = {10.1007/s00026-010-0057-2},
       opturl = {https://doi.org/10.1007/s00026-010-0057-2},
}  

@article {Fomin-Reading,
    AUTHOR = {Fomin, Sergey and Reading, Nathan},
     TITLE = {Root systems and generalized associahedra},
 BOOKTITLE = {Geometric combinatorics},
    SERIES = {IAS/Park City Math. Ser.},
    VOLUME = {13},
     PAGES = {63--131},
 PUBLISHER = {Amer. Math. Soc., Providence, RI},
      YEAR = {2007},
   MRCLASS = {20F55 (05E99 16S99 17B20 52B70)},
  MRNUMBER = {2383126},
}  

@article {Hetyei-tch,
    AUTHOR = {Hetyei, G\'{a}bor},
     TITLE = {Tchebyshev posets},
   JOURNAL = {Discrete Comput. Geom.},
  FJOURNAL = {Discrete \& Computational Geometry. An International Journal
              of Mathematics and Computer Science},
    VOLUME = {32},
      YEAR = {2004},
    NUMBER = {4},
     PAGES = {493--520},
      ISSN = {0179-5376},
   MRCLASS = {06A07 (52B22)},
  MRNUMBER = {2096745},
MRREVIEWER = {Margaret M. Bayer},
       DOI = {10.1007/s00454-004-1115-5},
       opturl = {https://doi.org/10.1007/s00454-004-1115-5},
} 

@article {Hetyei-mfp,
    AUTHOR = {Hetyei, G\'{a}bor},
     TITLE = {Matrices of formal power series associated to binomial posets},
   JOURNAL = {J. Algebraic Combin.},
  FJOURNAL = {Journal of Algebraic Combinatorics. An International Journal},
    VOLUME = {22},
      YEAR = {2005},
    NUMBER = {1},
     PAGES = {65--104},
      ISSN = {0925-9899},
   MRCLASS = {06A07 (05A15 05E25 16W60 52B05)},
  MRNUMBER = {2163710},
MRREVIEWER = {Joseph Kung},
       DOI = {10.1007/s10801-005-2506-2},
       opturl = {https://doi.org/10.1007/s10801-005-2506-2},
}  

@article {Hetyei-tt,
    AUTHOR = {Hetyei, G\'{a}bor},
     TITLE = {Tchebyshev triangulations of stable simplicial complexes},
   JOURNAL = {J. Combin. Theory Ser. A},
  FJOURNAL = {Journal of Combinatorial Theory. Series A},
    VOLUME = {115},
      YEAR = {2008},
    NUMBER = {4},
     PAGES = {569--592},
      ISSN = {0097-3165},
   MRCLASS = {52B70 (05A15 30C15 33C45 57Q15)},
  MRNUMBER = {2407914},
MRREVIEWER = {Margaret M. Bayer},
       DOI = {10.1016/j.jcta.2007.07.007},
       opturl = {https://doi.org/10.1016/j.jcta.2007.07.007},
}
  
@article {Hetyei-Nevo,
    AUTHOR = {Hetyei, G\'{a}bor and Nevo, Eran},
     TITLE = {Generalized {T}chebyshev triangulations},
   JOURNAL = {J. Combin. Theory Ser. A},
  FJOURNAL = {Journal of Combinatorial Theory. Series A},
    VOLUME = {137},
      YEAR = {2016},
     PAGES = {88--125},
      ISSN = {0097-3165},
   MRCLASS = {05E45},
  MRNUMBER = {3403517},
MRREVIEWER = {Christian Stump},
       DOI = {10.1016/j.jcta.2015.08.004},
       opturl = {https://doi.org/10.1016/j.jcta.2015.08.004},
} 

@article {Hohlweg-Lange,
    AUTHOR = {Hohlweg, Christophe and Lange, Carsten E. M. C.},
     TITLE = {Realizations of the associahedron and cyclohedron},
   JOURNAL = {Discrete Comput. Geom.},
  FJOURNAL = {Discrete \& Computational Geometry. An International Journal
              of Mathematics and Computer Science},
    VOLUME = {37},
      YEAR = {2007},
    NUMBER = {4},
     PAGES = {517--543},
      ISSN = {0179-5376},
   MRCLASS = {52B40 (05E25 06B10 20F55 52C07 55U10)},
  MRNUMBER = {2321739},
MRREVIEWER = {Ricardo Strausz},
       DOI = {10.1007/s00454-007-1319-6},
       opturl = {https://doi.org/10.1007/s00454-007-1319-6},
}  

@article {Jojic,
    AUTHOR = {Joji\'{c}, Du\v{s}ko},
     TITLE = {The cd-index of the poset of intervals and
              {$E_t$}-construction},
   JOURNAL = {Rocky Mountain J. Math.},
  FJOURNAL = {The Rocky Mountain Journal of Mathematics},
    VOLUME = {40},
      YEAR = {2010},
    NUMBER = {2},
     PAGES = {527--541},
      ISSN = {0035-7596},
   MRCLASS = {06A07 (52B99)},
  MRNUMBER = {2646456},
MRREVIEWER = {G\'{a}bor Hetyei},
       DOI = {10.1216/RMJ-2010-40-2-527},
       opturl = {https://doi.org/10.1216/RMJ-2010-40-2-527},
}
@article {Loday,
    AUTHOR = {Loday, Jean-Louis},
     TITLE = {Realization of the {S}tasheff polytope},
   JOURNAL = {Arch. Math. (Basel)},
  FJOURNAL = {Archiv der Mathematik},
    VOLUME = {83},
      YEAR = {2004},
    NUMBER = {3},
     PAGES = {267--278},
      ISSN = {0003-889X},
   MRCLASS = {52B11 (55P47 55P48)},
  MRNUMBER = {2108555},
MRREVIEWER = {Richard John Steiner},
       DOI = {10.1007/s00013-004-1026-y},
       opturl = {https://doi.org/10.1007/s00013-004-1026-y},
}   

@article {Ma,
    AUTHOR = {Ma, Shi-Mei},
     TITLE = {A family of two-variable derivative polynomials for tangent
              and secant},
   JOURNAL = {Electron. J. Combin.},
  FJOURNAL = {Electronic Journal of Combinatorics},
    VOLUME = {20},
      YEAR = {2013},
    NUMBER = {1},
     PAGES = {Paper 11, 12},
   MRCLASS = {05A15 (05A05)},
  MRNUMBER = {3035021},
}

@misc{OEIS,
	title={The On-Line Encyclopedia of Integer Sequences},
	author={Sloane, N. J. A.},
	note={\url{https://oeis.org}}
}


@article {Postnikov,
    AUTHOR = {Postnikov, Alexander},
     TITLE = {Permutohedra, associahedra, and beyond},
   JOURNAL = {Int. Math. Res. Not. IMRN},
  FJOURNAL = {International Mathematics Research Notices. IMRN},
      YEAR = {2009},
    NUMBER = {6},
     PAGES = {1026--1106},
      ISSN = {1073-7928},
   MRCLASS = {05E30},
  MRNUMBER = {2487491},
       DOI = {10.1093/imrn/rnn153},
       opturl = {https://doi.org/10.1093/imrn/rnn153},
}
  
@book{Stanley-EC1,
    AUTHOR = {Stanley, Richard P.},
     TITLE = {Enumerative combinatorics. {V}olume 1},
    SERIES = {Cambridge Studies in Advanced Mathematics},
    VOLUME = {49},
   EDITION = {Second edition},
 PUBLISHER = {Cambridge University Press, Cambridge},
      YEAR = {2012},
     PAGES = {xiv+626},
      ISBN = {978-1-107-60262-5},
   MRCLASS = {05-02 (05A15 06-02)},
  MRNUMBER = {2868112},
}

@article {Stanley-flag,
    AUTHOR = {Stanley, Richard P.},
     TITLE = {Flag {$f$}-vectors and the {$cd$}-index},
   JOURNAL = {Math. Z.},
  FJOURNAL = {Mathematische Zeitschrift},
    VOLUME = {216},
      YEAR = {1994},
    NUMBER = {3},
     PAGES = {483--499},
      ISSN = {0025-5874},
   MRCLASS = {06A07 (06A08 52B05 52B20)},
  MRNUMBER = {1283084},
MRREVIEWER = {Glenn H. Hurlbert},
       DOI = {10.1007/BF02572336},
       opturl = {https://doi.org/10.1007/BF02572336},
}  

@article {Wachs-pt,
    AUTHOR = {Wachs, Michelle L.},
     TITLE = {Poset topology: tools and applications},
 BOOKTITLE = {Geometric combinatorics},
    SERIES = {IAS/Park City Math. Ser.},
    VOLUME = {13},
     PAGES = {497--615},
 PUBLISHER = {Amer. Math. Soc., Providence, RI},
      YEAR = {2007},
   MRCLASS = {06B30 (05E10 52C35 55R80)},
  MRNUMBER = {2383132},
}

@article {Walker,
    AUTHOR = {Walker, James W.},
     TITLE = {Canonical homeomorphisms of posets},
   JOURNAL = {European J. Combin.},
  FJOURNAL = {European Journal of Combinatorics},
    VOLUME = {9},
      YEAR = {1988},
    NUMBER = {2},
     PAGES = {97--107},
      ISSN = {0195-6698},
   MRCLASS = {06A10},
  MRNUMBER = {939858},
MRREVIEWER = {Hartmut H\"{o}ft},
       DOI = {10.1016/S0195-6698(88)80033-7},
       opturl = {https://doi.org/10.1016/S0195-6698(88)80033-7}
       }