@article{arkani2014amplituhedron,
  title={The amplituhedron},
  author={Arkani{-Hamed}, Nima and Trnka, Jaroslav},
  journal={Journal of High Energy Physics},
  volume={2014},
  number={10},
  pages={1--33},
  year={2014},
  publisher={Springer}
}

@article{arkani2018unwinding,
  title={Unwinding the amplituhedron in binary},
  author={Arkani{-Hamed}, Nima and Thomas, Hugh and Trnka, Jaroslav},
  journal={Journal of High Energy Physics},
  volume={2018},
  number={1},
  pages={1--41},
  year={2018},
  publisher={Springer}
}

@book{arkani2016grassmannian,
  title={Grassmannian {G}eometry of {S}cattering {A}mplitudes},
  author={Arkani{-Hamed}, Nima and Bourjaily, Jacob and Cachazo, Freddy and Goncharov, Alexander and Trnka, Jaroslav and Postnikov, Alexander},
  year={2016},
  publisher={Cambridge University Press}
}

@article{karp2020decompositions,
  title={Decompositions of amplituhedra},
  author={Karp, Steven N and Williams, Lauren K and Zhang, Yan X},
  journal={Annales de l’Institut Henri Poincar{\'e} D},
  volume={7},
  number={3},
  pages={303--363},
  year={2020}
}

@article{karp2019amplituhedron,
  title={The m=1 Amplituhedron and Cyclic Hyperplane Arrangements},
  author={Karp, Steven N and Williams, Lauren K},
  journal={International Mathematics Research Notices},
  volume={2019},
  number={5},
  pages={1401--1462},
  year={2019},
  publisher={Oxford University Press}
}

@article{mohammadi2021triangulations,
  title={Triangulations and canonical forms of amplituhedra: a fiber-based approach beyond polytopes},
  author={Mohammadi, Fatemeh and Monin, Leonid and Parisi, Matteo},
  journal={Communications in Mathematical Physics},
  volume={387},
  number={2},
  pages={927--972},
  year={2021},
  publisher={Springer}
}

@article{arkani2021eft,
  title={The {EFT}-hedron},
  author={Arkani{-Hamed}, Nima and Huang, Tzu-Chen and Huang, Yu-tin},
  journal={Journal of High Energy Physics},
  volume={2021},
  number={5},
  pages={1--108},
  year={2021},
  publisher={Springer}
}

@article{arkani2015shell,
  title={On-shell structures of {MHV} amplitudes beyond the planar limit},
  author={Arkani{-Hamed}, Nima and Bourjaily, Jacob L and Cachazo, Freddy and Postnikov, Alexander and Trnka, Jaroslav},
  journal={Journal of High Energy Physics},
  volume={2015},
  number={6},
  pages={1--16},
  year={2015},
  publisher={Springer}
}

@article{arkani2021stringy,
  title={Stringy canonical forms},
  author={Arkani{-Hamed}, Nima and He, Song and Lam, Thomas},
  journal={Journal of High Energy Physics},
  volume={2021},
  number={2},
  pages={1--62},
  year={2021},
  publisher={Springer}
}

@article{trnka2021towards,
  title={Towards the {G}ravituhedron: new expressions for {NMHV} gravity amplitudes},
  author={Trnka, Jaroslav},
  journal={Journal of High Energy Physics},
  volume={2021},
  number={4},
  pages={1--63},
  year={2021},
  publisher={Springer}
}

@article{arkani2018scattering,
  title={Scattering forms and the positive geometry of kinematics, color and the worldsheet},
  author={Arkani{-Hamed}, Nima and Bai, Yuntao and He, Song and Yan, Gongwang},
  journal={J. High Energy Physics},
  volume={2018},
  number={5},
  pages={1--78},
  year={2018},
  publisher={Springer}
}

@article{arkani2017positive,
  title={Positive geometries and canonical forms},
  author={Arkani{-Hamed}, Nima and Bai, Yuntao and Lam, Thomas},
  journal={Journal of High Energy Physics},
  volume={2017},
  number={11},
  pages={1--124},
  year={2017},
  publisher={Springer}
}

@article{arkani2019positive,
  title={On the positive geometry of conformal field theory},
  author={Arkani{-Hamed}, Nima and Huang, Yu-tin and Shao, Shu-Heng},
  journal={Journal of High Energy Physics},
  volume={2019},
  number={6},
  pages={1--48},
  year={2019},
  publisher={Springer}
}

@article{lukowski2019cluster,
  title={Cluster adjacency for m=2 {Y}angian invariants},
  author={{\L}ukowski, Tomasz and Parisi, Matteo and Spradlin, Marcus and Volovich, Anastasia},
  journal={Journal of High Energy Physics},
  volume={2019},
  number={10},
  pages={1--11},
  year={2019},
  publisher={Springer}
}

@misc{parisi2021m,
  title={The m=2 amplituhedron and the hypersimplex: signs, clusters, triangulations, {E}ulerian numbers},
  author={Parisi, Matteo and Sherman{-Bennett}, Melissa and Williams, Lauren},
  eprint={2104.08254},
  year={2021}
}

@article{galashin2020parity,
  title={Parity duality for the amplituhedron},
  author={Galashin, Pavel and Lam, Thomas},
  journal={Compositio Mathematica},
  volume={156},
  number={11},
  pages={2207--2262},
  year={2020},
  publisher={London Mathematical Society}
}

@article{lam2015totally,
  title={Totally nonnegative {G}rassmannian and {G}rassmann polytopes},
  author={Lam, Thomas},
  journal={Current Developments in Mathematics},
  volume={2014},
  number={1},
  pages={51--152},
  year={2014},
  publisher={International Press of Boston}
}


@article{britto2005new,
  title={New recursion relations for tree amplitudes of gluons},
  author={Britto, Ruth and Cachazo, Freddy and Feng, Bo},
  journal={Nuclear Physics B},
  volume={715},
  number={1-2},
  pages={499--522},
  year={2005},
  publisher={Elsevier}
}
	
@article{britto2005direct,
  title={Direct proof of the tree-level scattering amplitude recursion relation in {Y}ang--{M}ills theory},
  author={Britto, Ruth and Cachazo, Freddy and Feng, Bo and Witten, Edward},
  journal={Physical review letters},
  volume={94},
  number={18},
  pages={181602},
  year={2005},
  publisher={APS}
}

@article{fomin1999double,
  title={Double {B}ruhat cells and total positivity},
  author={Fomin, Sergey and Zelevinsky, Andrei},
  journal={Journal of the American Mathematical Society},
  volume={12},
  number={2},
  pages={335--380},
  year={1999}
}

@article{fomin2002cluster,
  title={Cluster algebras {I}: foundations},
  author={Fomin, Sergey and Zelevinsky, Andrei},
  journal={Journal of the American Mathematical Society},
  volume={15},
  number={2},
  pages={497--529},
  year={2002}
}

@article{fomin2003cluster,
  title={Cluster algebras {II}: Finite type classification},
  author={Fomin, Sergey and Zelevinsky, Andrei},
  journal={Inventiones Mathematicae},
  volume={154},
  number={1},
  pages={63},
  year={2003},
  publisher={Springer Nature BV}
}

@phdthesis{rietsch1998total,
  title={Total positivity and real flag varieties},
  author={Rietsch, Konstanze Christina},
  year={1998},
  school={Massachusetts Institute of Technology}
}

@inproceedings{postnikov2018positive,
  title={Positive {G}rassmannian and polyhedral subdivisions},
  author={Postnikov, Alexander},
  booktitle={Proc. of the International Congress of Mathematicians: Rio de Janeiro 2018},
  pages={3181--3211},
  year={2018},
  organization={World Scientific}
}

@misc{bao2019m,
  title={The m=2 amplituhedron},
  author={Bao, Huanchen and He, Xuhua},
  eprint={1909.06015},
  year={2019}
}

@incollection{lusztig1994total,
  title={Total positivity in reductive groups},
  author={Lusztig, George},
  booktitle={Lie theory and geometry},
  pages={531--568},
  year={1994},
  publisher={Springer}
}

@misc{postnikov2006total,
  title={Total positivity, Grassmannians, and networks},
  author={Postnikov, Alexander},
  eprint={math/0609764},
  year={2006}
}

@misc{lukowski2020positive,
  title={The positive tropical {G}rassmannian, the hypersimplex, and the m=2 amplituhedron},
  author={{\L}ukowski, Tomasz and Parisi, Matteo and Williams, Lauren K},
  eprint={2002.06164},
  year={2020}
}

@article{speyer2005tropical,
  title={The tropical totally positive {G}rassmannian},
  author={Speyer, David and Williams, Lauren},
  journal={Journal of Algebraic Combinatorics},
  volume={22},
  number={2},
  pages={189--210},
  year={2005},
  publisher={Springer}
}

@article{speyer2021positive,
  title={The positive {D}ressian equals the positive tropical {G}rassmannian},
  author={Speyer, David and Williams, Lauren},
  journal={Transactions of the American Mathematical Society, Series B},
  volume={8},
  number={11},
  pages={330--353},
  year={2021}
}

@article{marsh2004parametrizations,
  title={Parametrizations of flag varieties},
  author={Marsh, R and Rietsch, Konstanze},
  journal={Representation Theory of the American Mathematical Society},
  volume={8},
  number={9},
  pages={212--242},
  year={2004}
}

@incollection{kodama2013combinatorics,
  title={Combinatorics of {KP} solitons from the real {G}rassmannian},
  author={Kodama, Yuji and Williams, Lauren},
  booktitle={Algebras, Quivers and Representations},
  pages={155--193},
  year={2013},
  publisher={Springer}
}

@article{kodama2014kp,
  title={{KP} solitons and total positivity for the Grassmannian},
  author={Kodama, Yuji and Williams, Lauren},
  journal={Inventiones mathematicae},
  volume={198},
  number={3},
  pages={637--699},
  year={2014},
  publisher={Springer}
}

@misc{agarwala2021cancellation,
  title={Cancellation of spurious poles in {N}=4 {SYM}: physical and geometric},
  author={Agarwala, Susama and Marcott, Cameron},
  eprint={2105.00541},
  year={2021}
}

@article{rietsch2006closure,
  title={Closure relations for totally nonnegative cells in {G}/{P}},
  author={Rietsch, K},
  journal={Mathematical Research Letters},
  volume={13},
  number={5-6},
  pages={775--786},
  year={2006},
  publisher={International Press of Boston, Inc.}
}

@misc{williams2021positive,
  title={The positive {G}rassmannian, the amplituhedron, and cluster algebras},
  author={Williams, Lauren K},
  eprint={2110.10856},
  year={2021}
}

@article{agarwala2017wilson,
  title={Wilson loop diagrams and positroids},
  author={Agarwala, Susama and Marin{-Amat}, Eloi},
  journal={Communications in Mathematical Physics},
  volume={350},
  number={2},
  pages={569--601},
  year={2017},
  publisher={Springer}
}

@article{lam2008total,
  title={Total positivity for cominuscule {G}rassmannians},
  author={Lam, Thomas and Williams, Lauren},
  journal={New York J. Math},
  volume={14},
  pages={53--99},
  year={2008}
}

@article{lukowski2021boundaries,
  title={Boundaries of the Amplituhedron with amplituhedron{B}oundaries},
  author={{\L}ukowski, Tomasz and Moerman, Robert},
  journal={Computer Physics Communications},
  volume={259},
  pages={107653},
  year={2021},
  publisher={Elsevier}
}

@article{bai2015amplituhedron,
  title={The amplituhedron from momentum twistor diagrams},
  author={Bai, Yuntao and He, Song},
  journal={Journal of High Energy Physics},
  volume={2015},
  number={2},
  pages={1--39},
  year={2015},
  publisher={Springer}
}

@article{bourjaily2010efficient,
  title={Efficient tree-amplitudes in {N}=4: automatic {BCFW} recursion in {M}athematica},
  author={Bourjaily, Jacob L},
  journal={arXiv preprint arXiv:1011.2447},
  year={2010}
}

@article{galashin2022totally,
  title={The totally nonnegative Grassmannian is a ball},
  author={Galashin, Pavel and Karp, Steven N and Lam, Thomas},
  journal={Advances in Mathematics},
  volume={397},
  pages={108123},
  year={2022},
  publisher={Elsevier}
}

@article{postnikov2009matching,
  title={Matching polytopes, toric geometry, and the totally non-negative Grassmannian},
  author={Postnikov, Alexander and Speyer, David and Williams, Lauren},
  journal={Journal of Algebraic Combinatorics},
  volume={30},
  number={2},
  pages={173--191},
  year={2009},
  publisher={Springer}
}

@book{guillemin2010differential,
  title={Differential topology},
  author={Guillemin, Victor and Pollack, Alan},
  volume={370},
  year={2010},
  publisher={American Mathematical Soc.}
}

@article{thom1954quelques,
  title={Quelques propri{\'e}t{\'e}s globales des vari{\'e}t{\'e}s diff{\'e}rentiables},
  author={Thom, Ren{\'e}},
  journal={Commentarii Mathematici Helvetici},
  volume={28},
  number={1},
  pages={17--86},
  year={1954},
  publisher={Springer}
}

@article{hodges2013eliminating,
  title={Eliminating spurious poles from gauge-theoretic amplitudes},
  author={Hodges, Andrew},
  journal={Journal of High Energy Physics},
  volume={2013},
  number={5},
  pages={1--23},
  year={2013},
  publisher={Springer}
}

@misc{evenzohar2022bcfw,
  author = {Even{-Zohar}, Chaim and Lakrec, Tsviqa and Tessler, Ran J},
  license = {GPL-3.0},
  title = {{bcfw-amp}},
  url = {https://github.com/chaim-e/bcfw-amp},
  version = {1.0.0},
  year = {2022}
}

@article{sturmfels1988totally,
title = {Totally positive matrices and cyclic polytopes},
journal = {Linear Algebra and its Applications},
volume = {107},
pages = {275-281},
year = {1988},
issn = {0024-3795},
doi = {https://doi.org/10.1016/0024-3795(88)90250-9},
url = {https://www.sciencedirect.com/science/article/pii/0024379588902509},
author = {Bernd Sturmfels}
}

@misc{even2021amplituhedron,
  title={The Amplituhedron BCFW Triangulation},
  author={Even-Zohar, Chaim and Lakrec, Tsviqa and Tessler, Ran J},
  eprint={2112.02703},
  year={2021}
}

@misc{lam2022invitation,
  title={An invitation to positive geometries},
  author={Lam, Thomas},
  eprint={2208.05407},
  year={2022}
}

@article{rietsch1999algebraic,
  title={An algebraic cell decomposition of the nonnegative part of a flag variety},
  author={Rietsch, Konstanze},
  journal={Journal of algebra},
  volume={213},
  number={1},
  pages={144--154},
  year={1999},
  publisher={Elsevier}
}

@article{bourjaily2018amplituhedron,
  title={What is the Amplituhedron},
  author={Bourjaily, Jacob and Thomas, Hugh},
  journal={Not. Amer. Math. Soc},
  volume={65},
  pages={167},
  year={2018}
}

@article{williams2008total,
  title={Total positivity for cominuscule Grassmannians},
  author={Williams, Lauren and Lam, Thomas},
  journal={Discrete Mathematics \& Theoretical Computer Science},
  year={2008},
  publisher={Episciences. org}
}

@article{galashin2022regularity,
  title={Regularity theorem for totally nonnegative flag varieties},
  author={Galashin, Pavel and Karp, Steven and Lam, Thomas},
  journal={Journal of the American Mathematical Society},
  volume={35},
  number={2},
  pages={513--579},
  year={2022}
}