@article{PivPoly,
    AUTHOR = {Black, Alexander E. and De Loera, Jes\'us A. and L\"utjeharms,
              Niklas and Sanyal, Raman},
     TITLE = {The polyhedral geometry of pivot rules and monotone paths},
   JOURNAL = {SIAM J. Appl. Algebra Geom.},
  FJOURNAL = {SIAM Journal on Applied Algebra and Geometry},
    VOLUME = {7},
      YEAR = {2023},
    NUMBER = {3},
     PAGES = {623--650}, 
       DOI = {10.1137/22M1475910},
       URL = {https://doi.org/10.1137/22M1475910},
}

@article{GassSaaty,
  author =        {Gass, Saul and Saaty, Thomas},
  journal =       {Naval Res. Logist. Quart.},
  pages =         {39--45},
  title =         {The computational algorithm for the parametric
                   objective function},
  volume =        {2},
  year =          {1955},
  doi =           {10.1002/nav.3800020106},
  issn =          {0028-1441},
  url =           {https://doi.org/10.1002/nav.3800020106},
}

@article{CeballosSantosZiegler,
  author =        {Ceballos, Cesar and Santos, Francisco and
                   Ziegler, G\"{u}nter M.},
  journal =       {Combinatorica},
  number =        {5},
  pages =         {513--551},
  title =         {Many non-equivalent realizations of the
                   associahedron},
  volume =        {35},
  year =          {2015},
  doi =           {10.1007/s00493-014-2959-9},
  issn =          {0209-9683,1439-6912},
  url =           {https://doi.org/10.1007/s00493-014-2959-9},
}

@misc{BottmanPoliakova,
  author =        {Nathaniel Bottman and Daria Poliakova},
  year =  {2022},
  title =         {Constrainahedra},
  eprinttype = {arXiv},
  eprint = {2208.14529},
}

@book{Stasheff-book,
    AUTHOR = {Stasheff, James},
     TITLE = {{$H$}-spaces from a homotopy point of view},
    SERIES = {Lecture Notes in Mathematics},
    VOLUME = {Vol. 161},
 PUBLISHER = {Springer-Verlag, Berlin-New York},
      YEAR = {1970},
     PAGES = {v+95 pp.}, 
}

@article{Forcey,
  author =        {Forcey, Stefan},
  journal =       {Topology Appl.},
  number =        {2},
  pages =         {326--347},
  title =         {Convex hull realizations of the multiplihedra},
  volume =        {156},
  year =          {2008},
  doi =           {10.1016/j.topol.2008.07.010},
  issn =          {0166-8641},
  url =           {https://doi.org/10.1016/j.topol.2008.07.010},
}

@article{GenPermOrig,
  author =        {Postnikov, Alexander},
  journal =       {Int. Math. Res. Not. IMRN},
  number =        {6},
  pages =         {1026--1106},
  title =         {Permutohedra, associahedra, and beyond},
  year =          {2009},
  doi =           {10.1093/imrn/rnn153},
  issn =          {1073-7928,1687-0247},
  url =           {https://doi.org/10.1093/imrn/rnn153},
}

@article{ChapotonPilaud,
  author =        {Chapoton, Fr{\'e}d{\'e}ric and Pilaud, Vincent},
  journal =       {Ann. Henri Lebesgue},
  pages =         {1535--1601},
  title =         {Shuffles of deformed permutahedra, multiplihedra,
                   constrainahedra, and biassociahedra},
  volume =        {7},
  year =          {2024},
  doi =           {10.5802/ahl.225},
  issn =          {2644-9463},
  language =      {English},
}

@phdthesis{poliakova-thesis,
  author =        {Daria Poliakova},
  url =  {https://noter.math.ku.dk/phd21dp.pdf},
  school = {University of Copenhagen},
  title =         {Homotopical algebra and combinatorics of polytopes},
  year =          {2021},
}

@article{bottman,
  author =        {Bottman, Nathaniel},
  journal =       {Algebr. Geom. Topol.},
  number =        {2},
  pages =         {743--806},
  title =         {2-associahedra},
  volume =        {19},
  year =          {2019},
  doi =           {10.2140/agt.2019.19.743},
  issn =          {1472-2747,1472-2739},
  url =           {https://doi.org/10.2140/agt.2019.19.743},
}

@misc{germain_vincent,
  author =        {Vincent Pilaud and Germain Poullot},
  title =         {Pivot polytopes of products of simplices and shuffles
                   of associahedra},
  year =          {2024},
  eprinttype = {arXiv},
  eprint = {2410.12658},
}

@article{oeis,
  author =        {N. J. A. Sloane},
  url =       {https://oeis.org},
  title =         {The On-Line Encyclopedia of Integer Sequences},
  year =          {2022},
}

@manual{sage,
  author =        {W.\thinspace{}A. Stein and others},
  key =           {Sage},
  note =          {{\tt https://www.sagemath.org}},
  organization =  {The Sage Development Team},
  title =         {{S}age {M}athematics {S}oftware ({V}ersion 9.5)},
  year =          {2022},
}

@misc{PivotAsso,
  author =        {Alexander E. Black and Niklas L{\"u}tjeharms and
                   Raman Sanyal},
 eprinttype = {arXiv},  
  eprint = {2405.08506},
  title =         {From linear programming to colliding particles},
  year =          {2024},
}

@book{catalan,
    AUTHOR = {Stanley, Richard P.},
     TITLE = {Catalan numbers},
 PUBLISHER = {Cambridge University Press, New York},
      YEAR = {2015},
     PAGES = {viii+215},
       DOI = {10.1017/CBO9781139871495},
       URL = {https://doi.org/10.1017/CBO9781139871495},
}

@book{CRT,
  author =        {Beck, Matthias and Sanyal, Raman},
  pages =         {xiv+308},
  publisher =     {American Mathematical Society, Providence, RI},
  series =        {Graduate Studies in Mathematics},
  title =         {Combinatorial reciprocity theorems},
  volume =        {195},
  year =          {2018},
  doi =           {10.1090/gsm/195},
  isbn =          {978-1-4704-2200-4},
  url =           {https://doi.org/10.1090/gsm/195},
}

@book{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 pp.},
}