@article {armstrong2009generalized,
    AUTHOR = {Armstrong, Drew},
     TITLE = {Generalized noncrossing partitions and combinatorics of
              {C}oxeter groups},
   JOURNAL = {Mem. Amer. Math. Soc.},
  FJOURNAL = {Memoirs of the American Mathematical Society},
    VOLUME = {202},
      YEAR = {2009},
    NUMBER = {949},
     PAGES = {x+159},
      ISSN = {0065-9266,1947-6221},
      ISBN = {978-0-8218-4490-8},
   MRCLASS = {05-02 (05A17 05E15 05E18 06A06 20F55)},
  MRNUMBER = {2561274},
       DOI = {10.1090/S0065-9266-09-00565-1},
       URL = {https://doi.org/10.1090/S0065-9266-09-00565-1},
}

@book {bjorner2005combinatorics,
    AUTHOR = {Bj\"orner, Anders and Brenti, Francesco},
     TITLE = {Combinatorics of {C}oxeter groups},
    SERIES = {Graduate Texts in Mathematics},
    VOLUME = {231},
 PUBLISHER = {Springer, New York},
      YEAR = {2005},
     PAGES = {xiv+363},
      ISBN = {978-3540-442387; 3-540-44238-3},
   MRCLASS = {05-01 (05E15 20F55)},
  MRNUMBER = {2133266},
MRREVIEWER = {Jian-yi\ Shi},
}

@book {cartier1969problemes,
    AUTHOR = {Cartier, P. and Foata, D.},
     TITLE = {Probl\`emes combinatoires de commutation et
              r\'{e}arrangements},
    SERIES = {Lecture Notes in Mathematics},
    VOLUME = {No. 85},
 PUBLISHER = {Springer-Verlag, Berlin-New York},
      YEAR = {1969},
     PAGES = {iv+88},
   MRCLASS = {05.04},
  MRNUMBER = {239978},
MRREVIEWER = {J.\ B.\ Roberts},
DOI={10.1007/BFb0079468}
}

@book {dehornoy2015foundations,
    AUTHOR = {Dehornoy, Patrick and Digne, Fran\c{c}ois and Godelle, Eddy and
              Krammer, Daan and Michel, Jean},
     TITLE = {Foundations of {G}arside theory},
    SERIES = {EMS Tracts in Mathematics},
    VOLUME = {22},
 PUBLISHER = {European Mathematical Society (EMS), Z\"{u}rich},
      YEAR = {2015},
     PAGES = {xviii+691},
      ISBN = {978-3-03719-139-2},
   MRCLASS = {20Mxx (06F15 20F36 68Q42 68Q45)},
  MRNUMBER = {3362691},
MRREVIEWER = {Volker Gebhardt},
       DOI = {10.4171/139},
       URL = {https://doi.org/10.4171/139},
}

@article {dowling1973class,
    AUTHOR = {Dowling, T. A.},
     TITLE = {A class of geometric lattices based on finite groups},
   JOURNAL = {J. Combinatorial Theory Ser. B},
  FJOURNAL = {Journal of Combinatorial Theory. Series B},
    VOLUME = {14},
      YEAR = {1973},
     PAGES = {61--86},
      ISSN = {0095-8956},
   MRCLASS = {05B35},
  MRNUMBER = {307951},
MRREVIEWER = {Richard Stanley},
       DOI = {10.1016/s0095-8956(73)80007-3},
       URL = {https://doi.org/10.1016/s0095-8956(73)80007-3},
}

@misc{fu2024upho,
	author= {Fu, Ziyao and Peng, Yulin and Zhang, Yuchong},
	title = {The monoid representation of upho posets and total positivity},
	year = {2024},
	note = {In this volume of \emph{FPSAC '24 (Bochum)} abstracts}
}

@article{gao2020upho,
    AUTHOR = {Gao, Yibo and Guo, Joshua and Seetharaman, Karthik and Seidel,
              Ilaria},
     TITLE = {The rank-generating functions of upho posets},
   JOURNAL = {Discrete Math.},
  FJOURNAL = {Discrete Mathematics},
    VOLUME = {345},
      YEAR = {2022},
    NUMBER = {1},
     PAGES = {Paper No. 112629, 14},
      ISSN = {0012-365X},
   MRCLASS = {06A07 (05E05)},
  MRNUMBER = {4318812},
       DOI = {10.1016/j.disc.2021.112629},
       URL = {https://doi.org/10.1016/j.disc.2021.112629},
}

@article {hopkins2022note,
    AUTHOR = {Hopkins, Sam},
     TITLE = {A note on {M}\"{o}bius functions of upho posets},
   JOURNAL = {Electron. J. Combin.},
  FJOURNAL = {Electronic Journal of Combinatorics},
    VOLUME = {29},
      YEAR = {2022},
    NUMBER = {2},
     PAGES = {Paper No. 2.39, 6},
   MRCLASS = {06A07 (05A19)},
  MRNUMBER = {4432972},
MRREVIEWER = {Kevin Iv\'{a}n Piterman},
       DOI = {10.37236/11084},
       URL = {https://doi.org/10.37236/11084},
}

@misc {hopkins2024upho1,
    AUTHOR = {Hopkins, Sam},
     TITLE = {Upho lattices {I}: examples and non-examples of cores},
      YEAR = {2024},
      archivePrefix={arXiv},
    eprint = {2407.08013}
}

@misc {hopkins2024upho2,
    AUTHOR = {Hopkins, Sam and Lewis, Joel},
     TITLE = {Upho lattices {II}: ways of realizing a core},
      YEAR = {2024},
      NOTE = {In preparation}
}

@misc {hopkins2024upho3,
    AUTHOR = {Hopkins, Sam},
     TITLE = {Upho lattices {III}: distributive and modular lattices},
      YEAR = {2024},
      NOTE = {In preparation}
}

@article {stanley1972supersolvable,
    AUTHOR = {Stanley, R. P.},
     TITLE = {Supersolvable lattices},
   JOURNAL = {Algebra Universalis},
  FJOURNAL = {Algebra Universalis},
    VOLUME = {2},
      YEAR = {1972},
     PAGES = {197--217},
      ISSN = {0002-5240},
   MRCLASS = {06A20},
  MRNUMBER = {309815},
MRREVIEWER = {O. Frink},
       DOI = {10.1007/BF02945028},
       URL = {https://doi.org/10.1007/BF02945028},
}

@book {stanley2012ec1,
    AUTHOR = {Stanley, Richard P.},
     TITLE = {Enumerative combinatorics. {V}olume 1},
    SERIES = {Cambridge Studies in Advanced Mathematics},
    VOLUME = {49},
   EDITION = {Second},
 PUBLISHER = {Cambridge University Press, Cambridge},
      YEAR = {2012},
     PAGES = {xiv+626},
      ISBN = {978-1-107-60262-5},
   MRCLASS = {05-02 (05A15 06-02)},
  MRNUMBER = {2868112},
}

@misc{stanley2020upho,
author={Stanley, Richard P.},
title={From {S}tern's triangle to upper homogeneous posets},
year={2020},
howpublished={Talk transparencies, available at \url{https://math.mit.edu/~rstan/transparencies/stern-ml.pdf}},
}

@article {stanley2021rational,
author={Stanley, Richard P.},
title={Theorems and Conjectures on some rational generating functions},
   JOURNAL = {European J. Combin.},
  FJOURNAL = {European Journal of Combinatorics},
    VOLUME = {119},
      YEAR = {2024},
     PAGES = {Paper No. 103814},
       DOI = {10.1016/j.ejc.2023.103814}
}

@manual{sagemath,
  Key          = {SageMath},
  Author       = {{The Sage Developers}},
  Title        = {{S}ageMath, the {S}age {M}athematics {S}oftware {S}ystem ({V}ersion 10.2)},
  note         = {\url{https://www.sagemath.org}},
  Year         = {2023},
}
.