%% This BibTeX bibliography file was created using BibDesk.
%% http://bibdesk.sourceforge.net/



@article{armstrong2013uniform,
  title={A uniform bijection between nonnesting and noncrossing partitions},
  author={Armstrong, D. and Stump, C. and Thomas, H.},
  journal={Trans. Amer. Math. Soc.},
  volume={365},
  number={8},
  pages={4121--4151},
  year={2013},
}

@article{barrett2004discrete,
  title={Discrete dynamical systems on graphs and {B}oolean functions},
  author={Barrett, C. and Chen, W. and Zheng, M.},
  journal={Mathematics and Computers in Simulation},
  volume={66},
  number={6},
  pages={487--497},
  year={2004},
  publisher={Elsevier}
}

@article{biane2002parking,
  title={Parking functions of types {A} and {B}},
  author={Biane, P.},
  journal={Electron. J. Combin},
  volume={9},
  number={1},
  pages={N7},
  year={2002}
}

@book{bjorner2005combinatorics,
Address = {New York},
Author = {Bj{\"o}rner, A. and Brenti, F.},
Publisher = {Springer Verlag},
Title = {Combinatorics of {C}oxeter groups},
Year = {2005}
}

@article{brouwer1974period,
  title={On the period of an operator, defined on antichains},
  author={Brouwer, A. and Schrijver, L.},
  journal={Stichting Mathematisch Centrum. Zuivere Wiskunde},
  number={ZW 24/74},
  pages={1--13},
  year={1974},
  publisher={Stichting Mathematisch Centrum}
}

@article{cai2017q-stirling,
  title={$q$-{S}tirling numbers: A new view},
  author={Cai, Y. and Readdy, M.},
  journal={Advances in Applied Mathematics},
  volume={86},
  pages={50--80},
  year={2017},
  publisher={Elsevier}
}

@article{callan2007bijections,
  title={Bijections from {D}yck paths to 321-avoiding permutations revisited},
  author={Callan, D.},
  journal={Preprint},
  note={\arxiv{0711.2684v1}},
  year={2007}
}

@article {cameron1995orbits,
    AUTHOR = {Cameron, P. and Fon{-}Der{-}Flaass, D.},
     TITLE = {Orbits of antichains revisited},
   JOURNAL = {European J. Combin.},
  FJOURNAL = {European Journal of Combinatorics},
    VOLUME = {16},
      YEAR = {1995},
    NUMBER = {6},
     PAGES = {545--554},
}

@article{cook2004universality,
  title={Universality in elementary cellular automata},
  author={Cook, Matthew},
  journal={Complex Systems},
  volume={15},
  number={1},
  pages={1--40},
  year={2004},
}

 @inproceedings{david2021toggling,
author = {David, L. and Defant, C. and Joseph, M. and Macauley, M. and McDonough, A.},
title = {Dynamical algebraic combinatorics, asynchronous cellular automata, and toggling independent sets},
booktitle={Proc. 27th Intl. Workshop Cell. Autom. Discrete Compl. Syst. (AUTOMATA)},
year = {2021},
volume = {90},
number = {5},
pages = {1--16},
}

@article{defant2018flexible,
  title={Flexible toggles and symmetric invertible asynchronous elementary cellular automata},
  author={Defant, C.},
  journal={Discrete Math.},
  volume={341},
  number={9},
  pages={2367--2379},
  year={2018},
}

@article{develin2016toric,
  author = {Develin, M. and Macauley, M. and Reiner, V.},
  title = {Toric partial orders},
  journal = {Trans. Amer. Math. Soc.},
  volume = {368},
  number = {4},
  pages = {2263--2287},
  year = {2016}
  }

@incollection{deza1990loops,
  title={Loops of clutters},
  author={Deza, M.M. and Fukuda, K.},
  booktitle={Coding theory and design theory},
  pages={72--92},
  year={1990},
  publisher={Springer}
}

@article{dilks2017resonance,
  title={Resonance in orbits of plane partitions and increasing tableaux},
  author={Dilks, K. and Pechenik, O. and Striker, J.},
  journal={J. Comb. Theory Ser. A},
  volume={148},
  pages={244--274},
  year={2017},
}

@article{einstein2016noncrossing,
  title={Noncrossing partitions, toggles, and homomesies},
  author={Einstein, D. and Farber, M. and Gunawan, E. and Joseph, M. and Macauley, M. and Propp, J. and Rubinstein-Salzedo, S.},
journal = {Electron. J. Combin.},
volume = {23},
number = {3},
year = {2016},
}

@article{einstein2018combinatorial,
  title={Combinatorial, piecewise-linear, and birational homomesy for products of two chains},
  author={Einstein, D. and Propp, J.},
  journal={\arxiv{1310.5294v3}},
  year={2018}
}

@article{eriksson2009conjugacy,
Author = {Eriksson, H. and Eriksson, K.},
Journal = {Electron. J. Combin.},
Number = {2},
Pages = {\#R4},
Title = {Conjugacy of {C}oxeter elements},
Volume = {16},
Year = {2009}
}

@article{etienne1984linear,
  title={Linear extensions of finite posets and a conjecture of {G}.\ {K}reweras on permutations},
  author={Etienne, G.},
  journal={Discrete mathematics},
  volume={52},
  number={1},
  pages={107--111},
  year={1984},
  publisher={Elsevier}
}

@article{goulden2002tree-like,
  title={Tree-like properties of cycle factorizations},
  author={Goulden, I. and Yong, A.},
  journal={Journal of Combinatorial Theory, Series A},
  volume={98},
  number={1},
  pages={106--117},
  year={2002},
  publisher={Elsevier}
}

@article{grinberg2014iterative,
  title={Iterative properties of birational rowmotion},
  author={Grinberg, D. and Roby, T.},
  journal={\arxiv{1402.6178v6}},
  year={2014}
}

@article{haddadan2016some,
  title={Some Instances of Homomesy Among Ideals of Posets},
  author={Haddadan, S.},
  journal={\arxiv{1410.4819v3}},
  year={2016}
}

@article{heitsch2015counting,
author = {Heitsch, C.},
title = {Counting orbits under {K}reweras complementation},
note = {In preparation},
}

@article{hopkins2019minuscule,
  title={Minuscule doppelg{\"a}ngers, the coincidental down-degree expectations property, and rowmotion},
  author={Hopkins, S.},
  journal={Experimental Mathematics},
  pages={1--29},
  year={2020},
  publisher={Taylor \& Francis},
  note={Also available at \arxiv{1902.07301v3}.}
}

@article{hutchinson1963partitioning,
  title={Partitioning algorithms for finite sets},
  author={Hutchinson, G.},
  journal={Communications of the ACM},
  volume={6},
  number={10},
  pages={613--614},
  year={1963},
  publisher={ACM}
}

@inproceedings{ilie2015computation,
  title={Computation of {S}tirling numbers and generalizations},
  author={Ilie, S. and Jeffrey, D. and Corless, R. and Zhang, X.},
  booktitle={Symbolic and Numeric Algorithms for Scientific Computing (SYNASC), 2015 17th International Symposium on},
  pages={57--60},
  year={2015},
  organization={IEEE}
}

@article{joseph2018toggling,
  title={Toggling Independent Sets of a Path Graph},
  author={Joseph, M. and Roby, T.},
  journal={Electron J. Combin.},
  volume={25},
  number={1},
  pages={1--18},
  year={2018},
}
@article{joseph2019antichain,
  title={Antichain toggling and rowmotion},
  author={Joseph, M.},
  journal={Electron. J. Combin.},
  volume={26},
  number={1},
  year={2019},
}
@article{whirling,
author = {Joseph, M. and Propp, J. and Roby, T.},
title = {Whirling injections, surjections, and other families of finite-set functions},
note = {In preparation},
}
@article{joseph2020birational,
Author={Joseph, M. and Roby, T.},
Title = {A Birational lifting of the {S}tanley--{T}homas word on products of two chains},
journal={Preprint},
note={\arxiv{2001.03811}},
year={2020}
}
@article{joseph2020birational,
  title={Birational and noncommutative lifts of antichain toggling and rowmotion},
  author={Joseph, M. and Roby, T.},
  journal={Preprint},                  
  note={\arxiv{1909.09658v3}},
  year={2020}
}

@article{kirillov1995groups,
  title={Groups generated by involutions, {G}elfand--{T}setlin patterns, and combinatorics of {Y}oung tableaux},
  author={Kirillov, A. and Berenstein, A.},
  journal={Algebra i Analiz},
  volume={7},
  number={1},
  pages={92--152},
  year={1995},
  note={Translation available at \url{http://pages.uoregon.edu/arkadiy/bk1.pdf}.}
}

@article{kleiner2007admissible,
    AUTHOR = {Kleiner, M. and Pelley, A.},
     TITLE = {Admissible sequences, preprojective representations of
              quivers, and reduced words in the {W}eyl group of a
              {K}ac-{M}oody algebra},
   JOURNAL = {Int. Math. Res. Not. IMRN},
  FJOURNAL = {International Mathematics Research Notices. IMRN},
      YEAR = {2007},
    NUMBER = {4},
     PAGES = {Art. ID rnm013, 28},
      ISSN = {1073-7928},
   MRCLASS = {16G20 (05E15)},
  MRNUMBER = {2338197 (2008f:16035)},
MRREVIEWER = {Alistair Savage},
       DOI = {10.1093/imrn/rnm013},
       URL = {http://dx.doi.org/10.1093/imrn/rnm013},
}

@article{konheim1966occupancy,
  title={An occupancy discipline and applications},
  author={Konheim, A. and Weiss, B.},
  journal={SIAM Journal on Applied Mathematics},
  volume={14},
  number={6},
  pages={1266--1274},
  year={1966},
  publisher={SIAM}
}

@article{kreweras1970eventails,
  title={Sur les {\'e}ventails de segments},
  author={Kreweras, G.},
  journal={Cahiers du Bureau universitaire de recherche op{\'e}rationnelle S{\'e}rie Recherche},
  volume={15},
  pages={3--41},
  year={1970}
}
@article{kreweras1972partitions,
    AUTHOR = {Kreweras, G.},
     TITLE = {Sur les partitions non crois\'ees d'un cycle},
   JOURNAL = {Discrete Math.},
  FJOURNAL = {Discrete Mathematics},
    VOLUME = {1},
      YEAR = {1972},
    NUMBER = {4},
     PAGES = {333--350},
      ISSN = {0012-365X},
   MRCLASS = {05A17 (06A20)},
  MRNUMBER = {0309747 (46 \#8852)},
MRREVIEWER = {R. J. Wilson},
}



@article{lalanne1992involution,
  title={Une involution sur les chemins de {D}yck},
  author={Lalanne, J.C.},
  journal={European journal of combinatorics},
  volume={13},
  number={6},
  pages={477--487},
  year={1992},
  publisher={Academic Press}
}

@article{macauley2008order,
 author    = {Macauley, M. and McCammond, J. and Mortveit, H.S.},
 title     = {Order Independence in Asynchronous Cellular Automata},
 journal   = {J. Cell. Autom.},
 year      = {2008},
 volume    = {3},
 number    = {1},
 pages     = {37--56}
}
@article{macauley2009cycle,
 author    = {Macauley, M. and Mortveit, H.S.},
 title     = {Cycle Equivalence of Graph Dynamical Systems},
 journal   = {Nonlinearity},
 volume    = {22},
 pages     = {421--436},
 year      = {2009}
}
@article{macauley2011admissible,
  author = {Macauley, M. and Mortveit, H.},
  title = {Posets from admissible {C}oxeter sequences},
  journal = {Electron. J. Combin.},
  volume = {18},
  number = {1},
  pages = {\#R197},
  year = {2011}
  }
@article{macauley2011dynamics,
  title={Dynamics groups of asynchronous cellular automata},
  author={Macauley, M. and McCammond, J. and Mortveit, H.},
  journal={J. Algebraic Combin.},
  volume={33},
  number={1},
  pages={11--35},
  year={2011},
  publisher={Springer}
}

@article{mccammond2006noncrossing,
  author = {McCammond, J.},
  title = {Noncrossing partitions in surprising locations},
  journal = {Amer. Math. Monthly},
  volume = {113},
  year = {2006},
  number = {7},
  pages = {598-610},
  }

@article{mortveit2001discrete,
  title={Discrete, sequential dynamical systems},
  author={Mortveit, H.S. and Reidys, C.M.},
  journal={Discrete Math.},
  volume={226},
  number={1-3},
  pages={281--295},
  year={2001},
}
@book{mortveit2007introduction,
 author = {Mortveit, H.S. and Reidys, C.M.},
 title = {An Introduction to Sequential Dynamical Systems},
 publisher = {Springer Verlag},
 series = {Universitext},
 year = {2007},
}

@article{musiker2018paths,
  title={Paths to Understanding Birational Rowmotion on Products of Two Chains},
  author={Musiker, G. and Roby, T.},
  journal={\arxiv{1801.03877v3}},
  year={2018}
}

@article{numata2021action,
  title={On the action of the toggle group of the {D}ynkin diagram of type {A}},
  author={Numata, Y. and Yamanouchi, Y.},
  journal={\arxiv{2103.16217}},
  year={2021}
}

@article{panyushev2004ad-nilpotent,
  title={Ad-nilpotent ideals of a {B}orel subalgebra: generators and duality},
  author={Panyushev, D.},
  journal={J. Algebra},
  volume={274},
  pages={822--846},
  year={2004},
  note={Also available at \arxiv{0303107v1}.}
}
@article{panyushev2009orbits,
  title={On orbits of antichains of positive roots},
  author={Panyushev, D.},
  journal={European J. Combin.},
  volume={30},
  number={2},
  pages={586--594},
  year={2009},
  publisher={Elsevier},
  note={Also available at \arxiv{0711.3353v2}.}
}

@book{petersen2015eulerian,
Address = {New York},
Author = {Petersen, T. K.},
Publisher = {Springer},
Title = {Eulerian Numbers},
Year = {2015}
}

@article{pretzel1986reorienting,
  title={On reorienting graphs by pushing down maximal vertices},
  author={Pretzel, O.},
  journal={Order},
  volume={3},
  number={2},
  pages={135--153},
  year={1986},
}

@article{propp2015homomesy,
author = {Propp, J. and Roby, T.},
title = {Homomesy in Products of Two Chains},
journal = {Electron. J. Combin.},
volume = {22},
number = {3},
year = {2015},
}
@misc{propp2021spectral,
  title={Spectral theory for combinatorial dynamics},
  author={Propp, James},
  year={2021},
}

@article{reiner2004cyclic,
  title={The cyclic sieving phenomenon},
  author={Reiner, V. and Stanton, D. and White, D.},
  journal={Journal of Combinatorial Theory, Series A},
  volume={108},
  number={1},
  pages={17--50},
  year={2004},
  publisher={Elsevier}
}
@article{reiner2014what,
  title={What is\dots cyclic sieving},
  author={Reiner, V. and Stanton, D. and White, D.},
  journal={Notices Amer. Math. Soc},
  volume={61},
  number={2},
  pages={169--171},
  year={2014},
  publisher={}
}

@article{riordan1969ballots,
  title={Ballots and trees},
  author={Riordan, J.},
  journal={Journal of Combinatorial Theory},
  volume={6},
  number={4},
  pages={408--411},
  year={1969},
  publisher={Elsevier}
}

@article{reidys2001acyclic,
  title={On acyclic orientations and sequential dynamical systems},
  author={Reidys, Christian M},
  journal={Advances in Applied Mathematics},
  volume={27},
  number={4},
  pages={790--804},
  year={2001},
  publisher={Academic Press}
}

@incollection{roby2016dynamical,
  title={Dynamical algebraic combinatorics and the homomesy phenomenon},
  author={Roby, T.},
  booktitle={Recent Trends in Combinatorics},
  pages={619--652},
  year={2016},
  publisher={Springer},
}

@article{rush2015orbits,
  title={On orbits of order ideals of minuscule posets {II}: Homomesy},
  author={Rush, D. and Wang, K.},
  journal={\arxiv{1509.08047}},
  year={2015}
}

@article{sagan2011cyclic,
  title={The Cyclic Sieving Phenomenon: A Survey},
  author={Sagan, B.},
  journal={London Math. Soc. Lecture Note Ser},
  volume={392},
  pages={183-233},
  year={2011},
  note={Also available at \arxiv{1008.0790v3}.}
}

@article{salo2018universal,
  title={Universal gates with wires in a row},
  author={Salo, V.},
  journal={\arxiv{1809.08050}},
  year={2018}
}

@article{schonfisch1999synchronous,
  title={Synchronous and asynchronous updating in cellular automata},
  author={Sch{\"o}nfisch, B. and de Roos, A.},
  journal={BioSystems},
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  number={3},
  pages={123--143},
  year={1999},
  publisher={Elsevier}
}

@article {schutzenberger1963quelques,
    AUTHOR = {Sch{\"u}tzenberger, M.},
     TITLE = {Quelques remarques sur une construction de {S}chensted},
   JOURNAL = {Math. Scand.},
  FJOURNAL = {Mathematica Scandinavica},
    VOLUME = {12},
      YEAR = {1963},
     PAGES = {117--128},
      ISSN = {0025-5521},
   MRCLASS = {05.24},
  MRNUMBER = {0190017},
MRREVIEWER = {W. E. Coppage},
}
@article {schutzenberger1972promotion,
  title={Promotion des morphismes d'ensembles ordonn{\'e}s},
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  year={1972},
  publisher={Elsevier}
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@article {shi1997enumeration,
    AUTHOR = {Shi, J.},
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  FJOURNAL = {Journal of Algebraic Combinatorics. An International Journal},
    VOLUME = {6},
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   MRCLASS = {20F55 (05C25)},
  MRNUMBER = {1436533 (98d:20048)},
MRREVIEWER = {Luis Paris},
       DOI = {10.1023/A:1008695121783},
       URL = {http://dx.doi.org/10.1023/A:1008695121783},
}

@article {simion91structure,
Author = {Simion, R. and Ullman, D.},
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@inproceedings{simon1988recognizable,
  title={Recognizable sets with multiplicities in the tropical semiring},
  author={Simon, I.},
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  organization={Springer}
}

@article{speyer2009powers,
Author = {Speyer, D.},
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Pages = {1295--1302},
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Volume = {137},
Year = {2009}
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@article{stanley1973acyclic,
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@book{stanley2011enumerative,
Author = {Stanley, R.},
Publisher = {Cambridge University Press},
Title = {Enumerative combinatorics, volume 1, 2nd edition},
Year = {2011},
note={Also available at \url{http://math.mit.edu/~rstan/ec/ec1/}.}
}

@book{stanley1999enumerative,
Author = {Stanley, R.},
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Year = {1999}
}

@article{stanley1997parking,
  title={Parking functions and noncrossing partitions},
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  number={2},
  pages={R20},
  year={1997}
}

@article {stanley2009promotion,
    AUTHOR = {Stanley, R.},
     TITLE = {Promotion and evacuation},
   JOURNAL = {Electron. J. Combin.},
  FJOURNAL = {Electronic Journal of Combinatorics},
    VOLUME = {16},
      YEAR = {2009},
    NUMBER = {2, Special volume in honor of Anders Bj\"{o}rner},
     PAGES = {Research Paper 9, 24},
}

@article{stanley1986two,
  title={Two poset polytopes},
  author={Stanley, R.},
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  volume={1},
  number={1},
  pages={9--23},
  year={1986},
  publisher={Springer}
}

@article{striker2012promotion,
author = {Striker, J. and Williams, N.},
title = {Promotion and rowmotion},
journal = {European J. Combin.},
volume = {33},
pages = {1919--1942},
year = {2012},
}

@article{striker2015toggle,
  title={The toggle group, homomesy, and the {R}azumov-{S}troganov correspondence},
  author={Striker, J.},
  journal={Electron. J. Combin.},
  volume={22},
  number={2},
  pages={P2--57},
  year={2015},
  note={Also available at \arxiv{1503.08898v2}.}
}

@article{striker2017dynamical,
  title={Dynamical algebraic combinatorics: promotion, rowmotion, and resonance},
  author={Striker, J.},
  journal={Notices Amer. Math. Soc.},
  volume={64},
  number={6},
  year={2017}
}

@article{striker2018rowmotion,
  title={Rowmotion and generalized toggle groups},
  author={Striker, J.},
  journal={Discrete Math. Theor. Comput. Sci.},
  volume={20},
  year={2018},
}

@article{thomas2019rowmotion,
  title={Rowmotion in slow motion},
  author={Thomas, H. and Williams, N.},
  journal={Proc. London Math. Soc.},
  volume={119},
  number={5},
  pages={1149--1178},
  year={2019},
  publisher={Wiley Online Library}
}

@article{tutte1954contribution,
 author = {Tutte, W.},
 title = {A contribution to the theory of chromatic polynomials},
 journal = {Canad. J. Math.},
 volume = {6},
 year = {1954},
 pages = {80--91}
 }
 
 @inproceedings{vielhaber2012computing,
  title={Computing by temporal order: asynchronous cellular automata},
  author={Vielhaber, M.},
  booktitle={AUTOMATA},
  publisher={Electron. Proc. Theor. Comput. Sci.},
  volume={90},
  year={2012},
  pages={166--176}
}
 
 @article{vorland2017homomesy,
  title={Homomesy in products of three chains and multidimensional recombination},
  author={Vorland, C.},
  journal={\arxiv{1705.02665v2}},
  year={2017}
}

@phdthesis{vorland2018multidimensional,
  author       = {Vorland, C.}, 
  title        = {Multidimensional Toggle Dynamics},
  school       = {North Dakota State University},
  year         = 2018,
}
 
@article{widthrestricted,
author={Walsh, D.},
title = {Width-restricted finite functions},
journal={\url{http://capone.mtsu.edu/dwalsh/width\_2.pdf}}
}

@book{wolfram1986theory,
  title={Theory and applications of cellular automata},
  author={Wolfram, S.},
  journal={World Scientific},
  year={1986}
}


%%%%% Manuals below

@manual{oeis,
 author = {N. Sloane},
 title = {OEIS, Online Encyclopedia of Integer Sequences},
 note = {\url{https://oeis.org/}},
 year = {2016},
 }

@manual{sage,
 author               = {W. Stein and others},
 key                  = {Sage},
 note                 = {\url{http://www.sagemath.org}},
 organization         = {The Sage Development Team},
 title                = {{S}age {M}athematics {S}oftware ({V}ersion 7.3)},
 year                 = {2016},
}