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@book{MaclaganDiane1974-author2015Ittg,
series = {Graduate studies in mathematics Volume 161},
issn = {9780821851982},
publisher = {Providence, Rhode Island : American Mathematical Society},
isbn = {9780821851982},
year = {2015},
title = {Introduction to tropical geometry},
language = {eng},
author = {Maclagan, Diane},
keywords = {Tropical geometry -- Study and teaching (Graduate); Geometry, Algebraic -- Study and teaching (Graduate)},
}
@book{CoxDavid2007IVaA,
series = {Undergraduate Texts in Mathematics},
publisher = {Springer},
isbn = {9780387356518},
year = {2007},
title = {Ideals, Varieties, and Algorithms [electronic resource] : An Introduction to Computational Algebraic Geometry and Commutative Algebra},
language = {eng},
address = {New York, NY},
author = {Cox, David},
keywords = {Computer software; Logic, Symbolic and mathematical; Algebra; Geometry, algebraic},
}
@book{ZieglerGunterM1995Lop,
series = {Graduate texts in mathematics ; 152},
publisher = {Springer-Verlag},
isbn = {9780387943657},
year = {1995},
title = {Lectures on polytopes},
language = {eng},
address = {New York},
author = {Ziegler, Günter M},
keywords = {Polytopes},
lccn = {94021784},
}
@misc{pin1998tropical,
title={Tropical semirings},
author={Pin, Jean-Eric},
year={1998}
}
@InProceedings{10.1007/BFb0017135,
author="Simon, Imre",
editor="Chytil, Michal P.
and Koubek, V{\'a}clav
and Janiga, Ladislav",
title="Recognizable sets with multiplicities in the tropical semiring",
booktitle="Mathematical Foundations of Computer Science 1988",
year="1988",
publisher="Springer Berlin Heidelberg",
address="Berlin, Heidelberg",
pages="107--120",
abstract="The last ten years saw the emergence of some results about recognizable subsets of a free monoid with multiplicities in the Min-Plus semiring. An interesting aspect of this theoretical body is that its discovery was motivated throughout by applications such as the finite power property, Eggan's classical star height problem and the measure of the nondeterministic complexity of finite automata. We review here these results, their applications and point out some open problems.",
isbn="978-3-540-45926-2"
}
@inproceedings{simon1978limited,
title={Limited subsets of a free monoid},
author={Simon, Imre},
booktitle={19th Annual Symposium on Foundations of Computer Science (sfcs 1978)},
pages={143--150},
year={1978},
organization={IEEE}
}
@article{klemperer2010product,
title={The product-mix auction: A new auction design for differentiated goods},
author={Klemperer, Paul},
journal={Journal of the European Economic Association},
volume={8},
number={2-3},
pages={526--536},
year={2010},
publisher={Oxford University Press}
}
@article{binmore2002biggest,
title={The biggest auction ever: The sale of the British 3G telecom licences},
author={Binmore, Ken and Klemperer, Paul},
journal={The Economic Journal},
volume={112},
number={478},
pages={C74--C96},
year={2002},
publisher={Oxford University Press Oxford, UK}
}
@article{baldwin2019understanding,
title={Understanding preferences:“demand types”, and the existence of equilibrium with indivisibilities},
author={Baldwin, Elizabeth and Klemperer, Paul},
journal={Econometrica},
volume={87},
number={3},
pages={867--932},
year={2019},
publisher={Wiley Online Library}
}
@book{lawson2003finite,
title={Finite automata},
author={Lawson, Mark V},
year={2003},
publisher={CRC Press}
}
@book{baker2016nonarchimedean,
title={Nonarchimedean and tropical geometry},
author={Baker, Matthew and Payne, Sam},
year={2016},
publisher={Springer}
}
@article{kato2014automata,
title={Automata in groups and dynamics and induced systems of PDE in tropical geometry},
author={Kato, Tsuyoshi},
journal={The Journal of Geometric Analysis},
volume={24},
number={2},
pages={901--987},
year={2014},
publisher={Springer}
}
@article{kalinin2018self,
title={Self-organized criticality and pattern emergence through the lens of tropical geometry},
author={Kalinin, Nikita and Guzm{\'a}n-S{\'a}enz, Aldo and Prieto, Yulieth and Shkolnikov, Mikhail and Kalinina, Vera and Lupercio, Ernesto},
journal={Proceedings of the National Academy of Sciences},
volume={115},
number={35},
pages={E8135--E8142},
year={2018},
publisher={National Acad Sciences}
}
@article{bak1987self,
title={Self-organized criticality: An explanation of the 1/f noise},
author={Bak, Per and Tang, Chao and Wiesenfeld, Kurt},
journal={Physical review letters},
volume={59},
number={4},
pages={381},
year={1987},
publisher={APS}
}
@article{bak1988self,
title={Self-organized criticality},
author={Bak, Per and Tang, Chao and Wiesenfeld, Kurt},
journal={Physical review A},
volume={38},
number={1},
pages={364},
year={1988},
publisher={APS}
}
@article{brown1969locally,
title={On locally finite semigroups},
author={Brown, TC},
journal={Ukrainian Mathematical Journal},
volume={20},
number={6},
pages={631--636},
year={1969}
}
@online{12Trop,
title = {Twelve Lectures on Tropical Geometry},
date = {2020},
organization = {Youtube},
author = {Bernd Sturmfels},
url = {https://www.youtube.com/playlist?list=PLRy_Pn1LtSpfYE39TuCZrJAi7-0z44sQB},
}