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@article{AST13,
author = {D. Armstrong and C. Stump and H. Thomas},
title = {A uniform bijection between nonnesting and non-crossing partitions},
journal = {Transactions of the American Mathematical Society}, 
number = {365},
volume = {8},
pages = {4121-–4151},
year ={2013}
}
@article{BS74, author = {A. Brouwer and A. Schrijver}, 
title = {On the period of an operator, defined on antichains},
journal = {Math Centrum report ZW}, 
volume ={24/74},
year = {1974}
}
@article{CF95, 
author = {P.J. Cameron and D.G. Fon-Der-Flaass},
title ={Orbits of antichains revisited},
journal ={European Journal of Combinatorics},
volume = {16},
number = {6},
pages = {545-–554},
year = {1995}
}
@article{DH21,
author = {C. Defant and S. Hopkins},
title ={Symmetry of Narayana numbers and rowvacuation of root posets},
journal = {Forum of Mathematics, Sigma},
volume={9},
year = {2021}
}
@article{EP1,
author = {S. Elizalde and I. Pak},
title ={Bijections for refined restricted permutations},
journal = {Journal Combinatorial Theory Series A},
volume = {105},
year = {2004},
pages = {207--219}
}
@misc{HJP, 
author ={S. Hopkins and M. Joseph},
title = {The birational Lalanne--Kreweras involution}, 
eprint= {2012.15795v1}, 
year = {2020}
}      
@article{HJ20, author = {S. Hopkins and M. Joseph}, 
title = {The birational Lalanne--Kreweras involution}, 
journal = {Algebraic Combinatorics}, 
volume = {5},
number ={2}, 
year = {2022},
pages ={227--265}}
@article{SW12, 
author = {J. Striker and N. Williams},
title = {Promotion and rowmotion},
journal = {European Journal of Combinatorics},
volume ={33},
year ={2012}, number= {8},
pages= {1919-–1942}
}

@article{KRE70,
author = {Kreweras, G.},
journal = {Cahiers du Bureau universitaire de recherche op\'{e}rationnelle S\'{e}rie Recherche},
pages = {3-41},
title = {Sur les \'{e}ventails de segments},
volume = {15},
year = {1970},
}
@article{PR15,
  title={Homomesy in Products of Two Chains},
  author={James Gary Propp and Tom Roby},
  journal={Electronic Journal of Combatorics},
  year={2015},
  volume={22},
  number = {3.4}
}
@article{PAN04,
title = {Ad-nilpotent ideals of a Borel subalgebra: generators and duality},
journal = {Journal of Algebra},
volume = {274},
number = {2},
pages = {822-846},
year = {2004},
author = {Dmitri I. Panyushev}
}
@article{PAN09,
title = {On orbits of antichains of positive roots},
journal = {European Journal of Combinatorics},
volume = {30},
number = {2},
pages = {586-594},
year = {2009},
author = {Dmitri I. Panyushev}}
@article{LAL92,
title = {Une involution sur les chemins de Dyck},
journal = {European Journal of Combinatorics},
volume = {13},
number = {6},
pages = {477-487},
year = {1992},
author = {J.C. Lalanne}
}
@book{EC2,  series={Cambridge Studies in Advanced Mathematics}, title={Enumerative Combinatorics}, volume={2},  publisher={Cambridge University Press}, author={Stanley, Richard P. }, year={1999}, collection={Cambridge Studies in Advanced Mathematics}
}
@article{SS85,
title = {Restricted Permutations},
journal = {European Journal of Combinatorics},
volume = {6},
number = {4},
pages = {383-406},
year = {1985},
author = {Rodica Simion and Frank W. Schmidt},
}
@article{RE05,
title = {Refined sign-balance on 321-avoiding permutations},
journal = {European Journal of Combinatorics},
volume = {26},
number = {6},
pages = {1009-1018},
year = {2005},
author = {Astrid Reifegerste},
}
@article{RHO10,
title = {Cyclic sieving, promotion, and representation theory},
journal = {Journal of Combinatorial Theory, Series A},
volume = {117},
number = {1},
pages = {38-76},
year = {2010},
author = {Brendon Rhoades}
}