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@article{ast,
	Author = {Armstrong, D. and Stump, C. and Thomas, H.},
	Date-Modified = {2019-05-28 15:41:11 +1000},
	Doi = {10.1090/s0002-9947-2013-05729-7},
	Journal = {Trans. Amer. Math. Soc.},
	Number = {8},
	Pages = {4121--4151},
	Title = {A uniform bijection between nonnesting and noncrossing partitions},
	Volume = {365},
	Year = {2013}}

@article{biane-parking-bij,
	Author = {Biane, P.},
	Journal = {Electron. J. Combin},
	Number = {1},
	Pages = {N7},
	Title = {Parking functions of types {A} and {B}},
	Volume = {9},
	Year = {2002}}

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

@article{brouwer1974period,
	Author = {Brouwer, A. and Schrijver, L.},
	Journal = {Stichting Mathematisch Centrum. Zuivere Wiskunde},
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	Pages = {1--13},
	Publisher = {Stichting Mathematisch Centrum},
	Title = {On the period of an operator, defined on antichains},
	Year = {1974}}

@article{cai-readdy-rg,
	Author = {Cai, Y. and Readdy, M.},
	Journal = {Advances in Applied Mathematics},
	Pages = {50--80},
	Publisher = {Elsevier},
	Title = {$q$-{S}tirling numbers: A new view},
	Volume = {86},
	Year = {2017}}

@article{cameronfonder,
	Author = {Cameron, P. and Fon{-}Der{-}Flaass, D.},
	Date-Modified = {2019-05-28 15:42:06 +1000},
	Doi = {10.1016/0195-6698(95)90036-5},
	Fjournal = {European Journal of Combinatorics},
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	Number = {6},
	Pages = {545--554},
	Title = {Orbits of antichains revisited},
	Volume = {16},
	Year = {1995}}

@misc{develin2015toric,
	Author = {Develin, M. and Macauley, M. and Reiner, V.},
	Note = {{\em Trans. Amer. Math. Soc.}, In press, 2015.},
	Title = {Toric partial orders},
	Year = {2015}}

@article{dpsresonance,
	Author = {Dilks, K. and Pechenik, O. and Striker, J.},
	Journal = {Journal of Combinatorial Theory, Series A},
	Pages = {244--274},
	Publisher = {Elsevier},
	Title = {Resonance in orbits of plane partitions and increasing tableaux},
	Volume = {148},
	Year = {2017}}

@article{efgjmpr,
	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.},
	Number = {3},
	Title = {Noncrossing partitions, toggles, and homomesies},
	Volume = {23},
	Year = {2016}}

@misc{einpropp,
	Author = {Einstein, D. and Propp, J.},
	Eprint = {1310.5294v3},
	Eprinttype = {arxiv},
	Title = {Combinatorial, piecewise-linear, and birational homomesy for products of two chains},
	Year = {2018}}

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

@article{etienne-84,
	Author = {Etienne, G.},
	Date-Modified = {2019-05-28 15:42:37 +1000},
	Doi = {10.1016/0012-365x(84)90108-0},
	Journal = {Discrete Math.},
	Number = {1},
	Pages = {107--111},
	Publisher = {Elsevier},
	Title = {Linear extensions of finite posets and a conjecture of {G}.\ {K}reweras on permutations},
	Volume = {52},
	Year = {1984}}

@misc{r-systems,
	Author = {Galashin, P. and Pylyavskyy, P.},
	Eprint = {1709.00578v1},
	Eprinttype = {arxiv},
	Title = {$ R $-systems},
	Year = {2017}}

@article{goulden-yong,
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	Journal = {Journal of Combinatorial Theory, Series A},
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	Publisher = {Elsevier},
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	Volume = {98},
	Year = {2002}}

@misc{grinberg-roby,
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	Eprint = {1402.6178v6},
	Eprinttype = {arxiv},
	Title = {Iterative properties of birational rowmotion},
	Year = {2014}}

@misc{shahrzad,
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	Eprint = {1410.4819v3},
	Eprinttype = {arxiv},
	Title = {Some Instances of Homomesy Among Ideals of Posets},
	Year = {2016}}

@article{heitsch2015counting,
	Author = {Heitsch, C.},
	Title = {Counting orbits under {K}reweras complementation}}

@article{hutchinson-rg,
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	Journal = {Communications of the ACM},
	Number = {10},
	Pages = {613--614},
	Publisher = {ACM},
	Title = {Partioning algorithms for finite sets},
	Volume = {6},
	Year = {1963}}

@inproceedings{r-associated,
	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},
	Organization = {IEEE},
	Pages = {57--60},
	Title = {Computation of {S}tirling numbers and generalizations},
	Year = {2015}}

@article{antichain-toggling,
	Author = {Joseph, M.},
	Date-Modified = {2019-05-28 15:44:42 +1000},
	Journal = {Electron J. Combin.},
	Number = {1},
	Pages = {P1.29, 43 pp},
	Title = {Antichain toggling and rowmotion},
	Url = {https://www.combinatorics.org/ojs/index.php/eljc/article/view/v26i1p29},
	Volume = {26},
	Year = {2019}}

@article{whirling,
	Author = {Joseph, M. and Propp, J. and Roby, T.},
	Title = {Whirling injections, surjections, and other families of finite-set functions}}

@article{indepsetspaper,
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	Date-Modified = {2019-05-28 15:45:29 +1000},
	Journal = {Electron J. Combin.},
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	Volume = {25},
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@article{berenstein,
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@article{kleiner2007admissible,
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@article{parking-functions-def,
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	Publisher = {SIAM},
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	Year = {1966}}

@article{kreweras1972sur,
	Author = {Kreweras, G.},
	Fjournal = {Discrete Mathematics},
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@article{macauley2011admissible,
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	Number = {1},
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	Title = {Posets from admissible {C}oxeter sequences},
	Volume = {18},
	Year = {2011}}

@article{mccammond2006noncrossing,
	Author = {McCammond, J.},
	Journal = {Amer. Math. Monthly},
	Number = {7},
	Pages = {598-610},
	Title = {Noncrossing partitions in surprising locations},
	Volume = {113},
	Year = {2006}}

@article{musiker-roby,
	Author = {Musiker, G. and Roby, T.},
	Date-Modified = {2019-05-28 15:46:06 +1000},
	Doi = {10.5802/alco.43},
	Journal = {Algebraic Comb.},
	Number = {2},
	Pages = {275-304},
	Title = {Paths to understanding birational rowmotion on products of two chains},
	Volume = {2},
	Year = {2019},
	Bdsk-Url-1 = {https://doi.org/10.5802/alco.43}}

@article{panyushev,
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	Pages = {586--594},
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	Title = {On orbits of antichains of positive roots},
	Volume = {30},
	Year = {2009}}

@book{peterseneulerian,
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	Author = {Petersen, T. K.},
	Publisher = {Springer},
	Title = {Eulerian Numbers},
	Year = {2015}}

@article{pretzel1986reorienting,
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@article{propproby,
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	Date-Modified = {2019-05-28 15:46:49 +1000},
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	Volume = {22},
	Year = {2015}}

@article{csp,
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	Date-Modified = {2019-05-28 15:47:40 +1000},
	Doi = {10.1016/j.jcta.2004.04.009},
	Journal = {J. Combin. Theory Ser. A},
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	Year = {2004}}

@article{csp-brief,
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@article{PF-formula-elegant-proof-pollak-riordan,
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@incollection{robydac,
	Author = {Roby, T.},
	Booktitle = {Recent Trends in Combinatorics},
	Date-Modified = {2019-05-28 15:48:10 +1000},
	Note = {Also available \href{http://www.math.uconn.edu/~troby/homomesyIMA2015Revised.pdf}{online}},
	Pages = {619--652},
	Publisher = {Springer},
	Title = {Dynamical algebraic combinatorics and the homomesy phenomenon},
	Year = {2016}}

@misc{rush-wang-homomesy-minuscule,
	Author = {Rush, D. and Wang, K.},
	Eprint = {1509.08047v1},
	Eprinttype = {arxiv},
	Title = {On orbits of order ideals of minuscule posets {II}: Homomesy},
	Year = {2015}}

@article{cspsagan,
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	Volume = {392},
	Year = {2011}}

@article{Sch63,
	Author = {Sch{\"u}tzenberger, M.},
	Fjournal = {Mathematica Scandinavica},
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@article{Sch72,
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@article{shi1997enumeration,
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@inproceedings{tropical-semiring,
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@article{stanley1973acyclic,
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@book{ec1ed2,
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@article{stanley-parking-bij,
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@article{Sta09,
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@article{strikergentog,
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@misc{vorland-3-chains,
	Author = {Vorland, C.},
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	Title = {Homomesy in products of three chains and multidimensional recombination},
	Year = {2017}}

@phdthesis{vorland-thesis,
	Author = {Vorland, C.},
	School = {North Dakota State University},
	Title = {Multidimensional Toggle Dynamics},
	Year = 2018}

@article{widthrestricted,
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	Journal = {\url{http://capone.mtsu.edu/dwalsh/width\_2.pdf}},
	Title = {Width-restricted finite functions}}

@article{Yil17,
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	Doi = {10.1007/s10468-018-9795-3},
	Journal = {Algebras and Representation Theory},
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	Publisher = {Springer},
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	Volume = {22},
	Year = {2017}}

@manual{oeis,
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@manual{sage,
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