@article {ARW, AUTHOR = {Ardila, Federico and Rinc{\'o}n, Felipe and Williams, Lauren}, TITLE = {Positroids and non-crossing partitions}, JOURNAL = {Trans. Amer. Math. Soc.}, FJOURNAL = {Transactions of the American Mathematical Society}, VOLUME = {368}, YEAR = {2016}, NUMBER = {1}, PAGES = {337--363}, MRCLASS = {05B35 (05A15 05A19 46L53)}, MRNUMBER = {3413866}, MRREVIEWER = {Anna de Mier}, DOI = {10.1090/tran/6331}, URL = {http://dx.doi.org/10.1090/tran/6331}, } @article{Morales, author={Gonzalez D'Leon, Rafael and Hanusa, Christopher and Morales, Alejandro and Yip, Martha}, title = "{Column convex matrices, G-cyclic orders, and flow polytopes}", journal = "\emph{\texttt{arXiv:2107.07326}}", archivePrefix = "arXiv", primaryClass = "math.CO", year = "2021" } @book {EC1, AUTHOR = {Stanley, Richard P.}, TITLE = {Enumerative combinatorics. {V}olume 1}, SERIES = {Cambridge Studies in Advanced Mathematics}, VOLUME = {49}, EDITION = {Second}, PUBLISHER = {Cambridge University Press, Cambridge}, YEAR = {2012}, PAGES = {xiv+626 pp.}, MRCLASS = {05-02 (05A15 06-02)}, MRNUMBER = {2868112}, } @book {macmahon, AUTHOR = {MacMahon, Major Percy A.}, TITLE = {Combinatory Analysis. {V}ol. {II}}, PUBLISHER = {Cambridge University Press, Cambridge}, YEAR = {1916}, PAGES = {xix+340 pp.}, } @article{maulik2006gromov, title={Gromov--{W}itten theory and {D}onaldson--{T}homas theory, {I}}, author={Maulik, Davesh and Nekrasov, Nikita and Okounkov, Andrei and Pandharipande, Rahul}, journal={Compositio Mathematica}, volume={142}, number={5}, pages={1263--1285}, year={2006}, publisher={London Mathematical Society} } @article{maulik2006gromov2, title={Gromov--witten theory and donaldson--thomas theory, {I}{I}}, author={Maulik, Davesh and Nekrasov, Nikita and Okounkov, Andrei and Pandharipande, Rahul}, journal={Compositio Mathematica}, volume={142}, number={5}, pages={1286--1304}, year={2006}, publisher={London Mathematical Society} } @article{gordon_davison_52, author = {M. Gordon and W. H. T. Davison}, title = {Theory of Resonance Topology of Fully Aromatic Hydrocarbons. {I}}, journal = {J. Chem. Phys.}, fjournal = {The Journal of Chemical Physics}, volume = {20}, number = {3}, pages = {428-435}, year = {1952}, doi = {10.1063/1.1700437}, URL = {http://dx.doi.org/10.1063/1.1700437}, } @article {MR1382733, AUTHOR = {Cheah, Jan}, TITLE = {On the cohomology of {H}ilbert schemes of points}, JOURNAL = {J. Algebraic Geom.}, FJOURNAL = {Journal of Algebraic Geometry}, VOLUME = {5}, YEAR = {1996}, NUMBER = {3}, PAGES = {479--511}, MRCLASS = {14C05 (14C30)}, MRNUMBER = {1382733}, MRREVIEWER = {Raquel\ Mallavibarrena}, } @article {bodroza_gutman_cyvin_tosic_1988, AUTHOR = {Bodro\v{z}a, O. and Gutman, I. and Cyvin, S. J. and To\v{s}i\'c, R.}, TITLE = {Number of {K}ekul\'e structures of hexagon-shaped benzenoids}, JOURNAL = {J. Math. Chem.}, FJOURNAL = {Journal of Mathematical Chemistry}, VOLUME = {2}, YEAR = {1988}, NUMBER = {3}, PAGES = {287--298}, MRCLASS = {92A40 (05C30)}, MRNUMBER = {966090}, MRREVIEWER = {N. Trinajsti\"A<87>}, DOI = {10.1007/BF01167208}, URL = {http://dx.doi.org/10.1007/BF01167208}, } @Article{cyvin_1986, author="Cyvin, Sven J.", title="The Number of \emph{Kekul\'{e}} Structures of Hexagon-shaped Benzenoids and Members of Other Related Classes", journal="Monatshefte f{\"u}r Chemie/Chemical Monthly", year="1986", volume="117", number="1", pages="33--45", abstract="Some results from the enumeration ofKekul{\'e} structures are reviewed; they pertain to parallelogram-shaped, bent strips, chevrons and symmetrical hexagon-shaped benzenoids. The existing formulas are extended to the class of asymmetrical hexagons. Applications of the new formula reproduces a number of known results for three-tier and four-tier strips. In the latter case also some new formulas are achieved.", issn="1434-4475", doi="10.1007/BF00809169", url="http://dx.doi.org/10.1007/BF00809169" } @book {kekule, AUTHOR = {Cyvin, S. J. and Gutman, I.}, TITLE = {Kekul\'e structures in benzenoid hydrocarbons}, SERIES = {Lecture notes in chemistry}, VOLUME = {46}, PUBLISHER = {Springer}, YEAR = {1988}, } @article {kekule_58, author = {Kekul\'{e}, August}, title = {Ueber die {C}onstitution und die {M}etamorphosen der chemischen {V}erbindungen und \"{u}ber die chemische {N}atur des {K}ohlenstoffs}, journal = {Annalen der Chemie und Pharmacie}, volume = {106}, number = {2}, publisher = {WILEY-VCH Verlag}, url = {http://dx.doi.org/10.1002/jlac.18581060202}, doi = {10.1002/jlac.18581060202}, pages = {129--159}, year = {1858}, } @article {hodge43, AUTHOR = {Hodge, W. V. D.}, TITLE = {Some enumerative results in the theory of forms}, JOURNAL = {Proc. Cambridge Philos. Soc.}, VOLUME = {39}, YEAR = {1943}, PAGES = {22--30}, MRCLASS = {09.0X}, MRNUMBER = {0007739}, MRREVIEWER = {O. Zariski}, } @incollection {WilliamsICM, AUTHOR = {Williams, Lauren K.}, TITLE = {The positive {G}rassmannian, the amplituhedron, and cluster algebras}, BOOKTITLE = {I{CM}---{I}nternational {C}ongress of {M}athematicians. {V}ol. {VI}. {S}ections 12--14}, PAGES = {4710--4737}, PUBLISHER = {EMS Press, Berlin}, YEAR = {[2023] \copyright 2023}, ISBN = {978-3-98547-064-8; 978-3-98547-564-3; 978-3-98547-058-7}, MRCLASS = {05E14 (13F60 14J81 14M15 14T15 52B40)}, MRNUMBER = {4680421}, } @article{KLEISS1989616, title = {Multigluon cross sections and 5-jet production at hadron colliders}, journal = {Nuclear Physics B}, volume = {312}, number = {3}, pages = {616-644}, year = {1989}, doi = {https://doi.org/10.1016/0550-3213(89)90574-9}, url = {https://www.sciencedirect.com/science/article/pii/0550321389905749}, author = {Ronald Kleiss and Hans Kuijf}, abstract = {} } @article{Cachazo:2018wvl, author = "Cachazo, Freddy and Early, Nick and Guevara, Alfredo and Mizera, Sebastian", title = "{$\Delta$-algebra and scattering amplitudes}", eprint = "1812.01168", archivePrefix = "arXiv", primaryClass = "hep-th", doi = "10.1007/JHEP02(2019)005", journal = "JHEP", volume = "02", pages = "005", year = "2019" } @article{Damgaard:2021qbi, author = "Damgaard, David and Ferro, Livia and Lukowski, Tomasz and Moerman, Robert", title = "{Kleiss-Kuijf relations from momentum amplituhedron geometry}", eprint = "2103.13908", archivePrefix = "arXiv", primaryClass = "hep-th", reportNumber = "LMU-ASC 07/21", doi = "10.1007/JHEP07(2021)111", journal = "JHEP", volume = "07", pages = "111", year = "2021" } @article{Cachazo:2023ltw, author = "Cachazo, Freddy and Early, Nick and Zhang, Yong", title = "{Generalized Color Orderings: CEGM Integrands and Decoupling Identities}", eprint = "2304.07351", archivePrefix = "arXiv", primaryClass = "hep-th", month = "4", year = "2023" } @article{Arkani-Hamed:2014bca, author = "Arkani-Hamed, Nima and Bourjaily, Jacob L. and Cachazo, Freddy and Postnikov, Alexander and Trnka, Jaroslav", title = "{On-Shell Structures of MHV Amplitudes Beyond the Planar Limit}", eprint = "1412.8475", archivePrefix = "arXiv", primaryClass = "hep-th", reportNumber = "CALT-TH-2014-169", doi = "10.1007/JHEP06(2015)179", journal = "JHEP", volume = "06", pages = "179", year = "2015" } @article{PTs, title = {Amplitude for $n$-Gluon Scattering}, author = {Parke, Stephen J. and Taylor, T. R.}, journal = {Phys. Rev. Lett.}, volume = {56}, issue = {23}, pages = {2459--2460}, numpages = {0}, year = {1986}, month = {Jun}, publisher = {American Physical Society}, doi = {10.1103/PhysRevLett.56.2459}, url = {https://link.aps.org/doi/10.1103/PhysRevLett.56.2459} } @article{Frost:2019fjn, author = "Frost, Hadleigh and Mason, Lionel", title = "{Lie polynomials and a twistorial correspondence for amplitudes}", primaryClass = "hep-th", doi = "10.1007/s11005-021-01483-1", journal = "Lett. Math. Phys.", volume = "111", number = "6", pages = "Art. no. 147", year = "2021" } @incollection {StanleyTriangulation, AUTHOR={Stanley, Richard}, TITLE = {Eulerian partitions of a unit hypercube}, BOOKTITLE = {Higher combinatorics: Proceedings of the {NATO} {A}dvanced {S}tudy {I}nstitute held in {B}erlin, {S}eptember 1-10, 1976}, EDITOR = {Aigner, Martin}, NOTE = {NATO Advanced Study Institute Series. Ser. C: Mathematical and Physical Sciences, 31}, PUBLISHER = {D. Reidel Publishing Co., Dordrecht-Boston, Mass.}, YEAR = {1977}, PAGES = {49}, } @book {SturmfelsGrobner, AUTHOR = {Sturmfels, Bernd}, TITLE = {Gr\"{o}bner bases and convex polytopes}, SERIES = {University Lecture Series}, VOLUME = {8}, PUBLISHER = {American Mathematical Society, Providence, RI}, YEAR = {1996}, PAGES = {xii+162 pp.}, MRCLASS = {13P10 (14M25 52B20)}, MRNUMBER = {1363949}, MRREVIEWER = {P. Schenzel}, DOI = {10.1090/ulect/008}, URL = {https://doi-org.ezp-prod1.hul.harvard.edu/10.1090/ulect/008}, } @article {LamPost, AUTHOR = {Lam, Thomas and Postnikov, Alexander}, TITLE = {Alcoved polytopes. {I}}, JOURNAL = {Discrete Comput. Geom.}, FJOURNAL = {Discrete \& Computational Geometry. An International Journal of Mathematics and Computer Science}, VOLUME = {38}, YEAR = {2007}, NUMBER = {3}, PAGES = {453--478}, MRCLASS = {52B12 (52B40)}, MRNUMBER = {2352704}, MRREVIEWER = {Jes\'{u}s A. De Loera}, DOI = {10.1007/s00454-006-1294-3}, } @book {bjornerbrenti, AUTHOR = {Bj\"{o}rner, Anders and Brenti, Francesco}, TITLE = {Combinatorics of {C}oxeter groups}, SERIES = {Graduate Texts in Mathematics}, VOLUME = {231}, PUBLISHER = {Springer, New York}, YEAR = {2005}, PAGES = {xiv+363 pp.}, ISBN = {978-3540-442387; 3-540-44238-3}, MRCLASS = {05-01 (05E15 20F55)}, MRNUMBER = {2133266}, MRREVIEWER = {Jian-yi Shi}, } @book {stanley_ec1, AUTHOR = {Stanley, Richard P.}, TITLE = {Enumerative combinatorics. {V}olume 1}, SERIES = {Cambridge Studies in Advanced Mathematics}, VOLUME = {49}, EDITION = {Second}, PUBLISHER = {Cambridge University Press, Cambridge}, YEAR = {2012}, PAGES = {xiv+626 pp.}, MRCLASS = {05-02 (05A15 06-02)}, MRNUMBER = {2868112}, } @article {tsukerman_williams, AUTHOR = {Tsukerman, E. and Williams, L.}, TITLE = {Bruhat interval polytopes}, JOURNAL = {Adv. Math.}, FJOURNAL = {Advances in Mathematics}, VOLUME = {285}, YEAR = {2015}, PAGES = {766--810}, MRCLASS = {52B40 (05A05 06A07 20F55 52B05)}, MRNUMBER = {3406515}, MRREVIEWER = {Joseph Kung}, DOI = {10.1016/j.aim.2015.07.030}, URL = {http://dx.doi.org/10.1016/j.aim.2015.07.030}, } @article {hodges, AUTHOR = {Hodges, Andrew}, TITLE = {Eliminating spurious poles from gauge-theoretic amplitudes}, JOURNAL = {J. High Energy Phys.}, FJOURNAL = {Journal of High Energy Physics}, YEAR = {2013}, VOLUME = {2013}, DOI = {10.1007/JHEP05(2013)135}, PAGES = {135, front matter+22 pp.}, } @article {fz-intel, AUTHOR = {Fomin, Sergey and Zelevinsky, Andrei}, TITLE = {Total positivity: tests and parametrizations}, JOURNAL = {Math. Intelligencer}, FJOURNAL = {The Mathematical Intelligencer}, VOLUME = {22}, YEAR = {2000}, NUMBER = {1}, PAGES = {23--33}, CODEN = {MAINDC}, MRCLASS = {15A48 (15A23 15A57 81R50)}, MRNUMBER = {1745560 (2001b:15030)}, MRREVIEWER = {D. J. Hartfiel}, DOI = {10.1007/BF03024444}, URL = {http://dx.doi.org/10.1007/BF03024444}, } @article {Karpman, AUTHOR = {Karpman, Rachel}, TITLE = {Bridge graphs and {D}eodhar parametrizations for positroid varieties}, JOURNAL = {J. Combin. Theory Ser. A}, FJOURNAL = {Journal of Combinatorial Theory. Series A}, VOLUME = {142}, YEAR = {2016}, PAGES = {113--146}, MRCLASS = {14M15 (05C10)}, MRNUMBER = {3499493}, MRREVIEWER = {Jacopo\ Gandini}, DOI = {10.1016/j.jcta.2016.03.005}, URL = {https://doi.org/10.1016/j.jcta.2016.03.005}, } @article{Drummond:2017ssj, author = "Drummond, James and Foster, Jack and G{\" u}rdo{\u g}an, {\" O}mer", title = "{Cluster Adjacency Properties of Scattering Amplitudes in $N=4$ Supersymmetric Yang-Mills Theory}", eprint = "1710.10953", archivePrefix = "arXiv", primaryClass = "hep-th", doi = "10.1103/PhysRevLett.120.161601", journal = "Phys. Rev. Lett.", volume = 120, number = 16, pages = 161601, year = 2018 } @article{Drummond:2018dfd, author = "Drummond, James and Foster, Jack and G{\"u}rdo{\u g}an, {\"O}mer", title = "{Cluster adjacency beyond MHV}", journal = "J. High Energy Physics", volume = "03", year = "2019", pages = "086", doi = "10.1007/JHEP03(2019)086", eprint = "1810.08149", archivePrefix = "arXiv", primaryClass = "hep-th", SLACcitation = "%%CITATION = ARXIV:1810.08149;%%" } @article{even2023cluster, title={Cluster algebras and Tilings for the m= 4 amplituhedron}, author={Even{-Zohar}, Chaim and Lakrec, Tsviqa and Parisi, Matteo and Tessler, Ran and Sherman-Bennett, Melissa and Williams, Lauren}, journal={arXiv preprint arXiv:2310.17727}, year={2023} } @article{Lukowski:2019sxw, AUTHOR = {{\L}ukowski, Tomasz}, title = "{On the boundaries of the $m=2$ amplituhedron}", eprint = "1908.00386", archivePrefix = "arXiv", primaryClass = "hep-th", doi = "10.4171/aihpd/124", journal = "Ann. Inst. H. Poincare D Comb. Phys. Interact.", volume = "9", number = "3", pages = "525--541", year = "2022" } @article{Cachazo:2013hca, author = "Cachazo, Freddy and He, Song and Yuan, Ellis Ye", title = "{Scattering of Massless Particles in Arbitrary Dimensions}", primaryClass = "hep-th", doi = "10.1103/PhysRevLett.113.171601", journal = "Phys. Rev. Lett.", volume = "113", number = "17", pages = "171601", year = "2014" } @article{ABL, author = "Arkani-Hamed, Nima and Bai, Yuntao and Lam, Thomas", title = "{Positive Geometries and Canonical Forms}", eprint = "1703.04541", archivePrefix = "arXiv", primaryClass = "hep-th", doi = "10.1007/JHEP11(2017)039", journal = "JHEP", volume = "11", pages = "039", year = "2017" } @article {KohnRanestad, AUTHOR = {Kohn, Kathl\'{e}n and Ranestad, Kristian}, TITLE = {Projective geometry of {W}achspress coordinates}, JOURNAL = {Found. Comput. Math.}, FJOURNAL = {Foundations of Computational Mathematics. The Journal of the Society for the Foundations of Computational Mathematics}, VOLUME = {20}, YEAR = {2020}, NUMBER = {5}, PAGES = {1135--1173}, MRCLASS = {52B11 (14J70 14N20 14N30 52B10 52C35)}, MRNUMBER = {4156995}, MRREVIEWER = {Raquel\ Mallavibarrena}, DOI = {10.1007/s10208-019-09441-z}, URL = {https://doi.org/10.1007/s10208-019-09441-z}, } @misc{BaoHe, eprinttype = {arXiv}, eprint = {1909.06015}, author = {Bao, Huanchen and He, Xuhua}, keywords = {Combinatorics (math.CO), High Energy Physics - Theory (hep-th), Representation Theory (math.RT), FOS: Mathematics, FOS: Mathematics, FOS: Physical sciences, FOS: Physical sciences}, title = {The m=2 amplituhedron}, year = {2019}, } @article {GSV, AUTHOR = {Gekhtman, Michael and Shapiro, Michael and Vainshtein, Alek}, TITLE = {On the properties of the exchange graph of a cluster algebra}, JOURNAL = {Math. Res. Lett.}, FJOURNAL = {Mathematical Research Letters}, VOLUME = {15}, YEAR = {2008}, NUMBER = {2}, PAGES = {321--330}, MRCLASS = {13A99}, MRNUMBER = {2385644}, MRREVIEWER = {David\ Smith}, DOI = {10.4310/MRL.2008.v15.n2.a10}, URL = {https://doi.org/10.4310/MRL.2008.v15.n2.a10}, } @article {SW21, AUTHOR = {Speyer, David and Williams, Lauren K.}, TITLE = {The positive {D}ressian equals the positive tropical {G}rassmannian}, JOURNAL = {Trans. Amer. Math. Soc. Ser. B}, FJOURNAL = {Transactions of the American Mathematical Society. Series B}, VOLUME = {8}, YEAR = {2021}, PAGES = {330--353}, MRCLASS = {14T15 (05E14 14M15 52C40)}, MRNUMBER = {4241765}, MRREVIEWER = {Margherita Barile}, DOI = {10.1090/btran/67}, } @article {OhSpeyer, AUTHOR = {Oh, Su Ho and Speyer, David E.}, TITLE = {Links in the complex of weakly separated collections}, JOURNAL = {J. Comb.}, FJOURNAL = {Journal of Combinatorics}, VOLUME = {8}, YEAR = {2017}, NUMBER = {4}, PAGES = {581--592}, MRCLASS = {05E15 (05B35 05E45)}, MRNUMBER = {3682392}, MRREVIEWER = {David J. Grabiner}, DOI = {10.4310/JOC.2017.v8.n4.a2}, URL = {https://doi-org.ezp-prod1.hul.harvard.edu/10.4310/JOC.2017.v8.n4.a2}, } @article {OPS, AUTHOR = {Oh, Suho and Postnikov, Alexander and Speyer, David E.}, TITLE = {Weak separation and plabic graphs}, JOURNAL = {Proc. Lond. Math. Soc. (3)}, FJOURNAL = {Proceedings of the London Mathematical Society. Third Series}, VOLUME = {110}, YEAR = {2015}, NUMBER = {3}, PAGES = {721--754}, DOI = {10.1112/plms/pdu052}, } @article {Muller-loc-acyc, AUTHOR = {Muller, Greg}, TITLE = {Locally acyclic cluster algebras}, JOURNAL = {Adv. Math.}, FJOURNAL = {Advances in Mathematics}, VOLUME = {233}, YEAR = {2013}, PAGES = {207--247}, DOI = {10.1016/j.aim.2012.10.002}, } @article {CL, AUTHOR = {Cao, Peigen and Li, Fang}, TITLE = {The enough {$g$}-pairs property and denominator vectors of cluster algebras}, JOURNAL = {Math. Ann.}, FJOURNAL = {Mathematische Annalen}, VOLUME = {377}, YEAR = {2020}, NUMBER = {3-4}, PAGES = {1547--1572}, DOI = {10.1007/s00208-020-02033-1}, } @article{AHTT, AUTHOR = {Arkani-Hamed, Nima and Thomas, Hugh and Trnka, Jaroslav}, TITLE = {Unwinding the amplituhedron in binary}, JOURNAL = {J. High Energy Phys.}, FJOURNAL = {Journal of High Energy Physics}, YEAR = {2018}, NUMBER = {1}, PAGES = {016, front matter+40 pp.}, MRCLASS = {81T60}, MRNUMBER = {3764259}, DOI = {10.1007/jhep01(2018)016}, URL = {https://doi.org/10.1007/jhep01(2018)016}, } @article {BCFW, AUTHOR = {Britto, Ruth and Cachazo, Freddy and Feng, Bo and Witten, Edward}, TITLE = {Direct proof of the tree-level scattering amplitude recursion relation in {Y}ang-{M}ills theory}, JOURNAL = {Phys. Rev. Lett.}, FJOURNAL = {Physical Review Letters}, VOLUME = {94}, YEAR = {2005}, NUMBER = {18}, PAGES = {181602, 4}, CODEN = {PRLTAO}, MRCLASS = {81T18 (81T13)}, MRNUMBER = {2260976}, DOI = {10.1103/PhysRevLett.94.181602}, URL = {http://dx.doi.org/10.1103/PhysRevLett.94.181602}, } @article{LKW, title={The positive Grassmannian, the amplituhedron, and cluster algebras}, author={Williams, Lauren}, journal={preprint arXiv:2110.10856}, year={2021} } @article{even2021amplituhedron, title={The Amplituhedron BCFW Triangulation}, author={Even{-Zohar}, Chaim and Lakrec, Tsviqa and Tessler, Ran J}, journal={full version of preprint arXiv:2112.02703}, year={2021} } @article {FZ1, AUTHOR = {Fomin, Sergey and Zelevinsky, Andrei}, TITLE = {Cluster algebras. {I}. {F}oundations}, JOURNAL = {J. Amer. Math. Soc.}, FJOURNAL = {Journal of the American Mathematical Society}, VOLUME = {15}, YEAR = {2002}, NUMBER = {2}, PAGES = {497--529 (electronic)}, MRCLASS = {16S99 (14M99 17B99)}, MRNUMBER = {1887642 (2003f:16050)}, MRREVIEWER = {Eric N. Sommers}, DOI = {10.1090/S0894-0347-01-00385-X}, URL = {http://dx.doi.org/10.1090/S0894-0347-01-00385-X}, } @article {marshscott, AUTHOR = {Marsh, R. J. and Scott, J. S.}, TITLE = {Twists of {P}l\"{u}cker coordinates as dimer partition functions}, JOURNAL = {Comm. Math. Phys.}, FJOURNAL = {Communications in Mathematical Physics}, VOLUME = {341}, YEAR = {2016}, NUMBER = {3}, PAGES = {821--884}, MRCLASS = {13F60 (14M15)}, MRNUMBER = {3452273}, MRREVIEWER = {Jianrong\ Li}, DOI = {10.1007/s00220-015-2493-7}, URL = {https://doi.org/10.1007/s00220-015-2493-7}, } @article {scott, AUTHOR = {Scott, Jeanne}, TITLE = {Grassmannians and cluster algebras}, JOURNAL = {Proc. London Math. Soc. (3)}, FJOURNAL = {Proceedings of the London Mathematical Society. Third Series}, VOLUME = {92}, YEAR = {2006}, NUMBER = {2}, PAGES = {345--380}, CODEN = {PLMTAL}, MRCLASS = {14M15 (05E15 16S99 22E46)}, MRNUMBER = {2205721 (2007e:14078)}, MRREVIEWER = {Eric N. Sommers}, DOI = {10.1112/S0024611505015571}, URL = {http://dx.doi.org/10.1112/S0024611505015571}, } @article {Fraser, AUTHOR = {Fraser, Chris}, TITLE = {Quasi-homomorphisms of cluster algebras}, JOURNAL = {Adv. in Appl. Math.}, FJOURNAL = {Advances in Applied Mathematics}, VOLUME = {81}, YEAR = {2016}, PAGES = {40--77}, MRCLASS = {13F60}, MRNUMBER = {3551663}, MRREVIEWER = {Yu Qiu}, DOI = {10.1016/j.aam.2016.06.005}, URL = {https://doi.org/10.1016/j.aam.2016.06.005}, } @article{OT10, AUTHOR = {Oppermann, Steffen and Thomas, Hugh}, TITLE = {Higher-dimensional cluster combinatorics and representation theory}, JOURNAL = {J. Eur. Math. Soc. (JEMS)}, FJOURNAL = {Journal of the European Mathematical Society (JEMS)}, VOLUME = {14}, YEAR = {2012}, NUMBER = {6}, PAGES = {1679--1737}, DOI = {10.4171/JEMS/345}, URL = {https://doi.org/10.4171/JEMS/345}, } @misc{OEIS, title={The {O}nline {E}ncyclopedia of {I}nteger {S}equences}, author={Sloane, Neil JA and others}, } @article {Fraser2, AUTHOR = {Fraser, Chris}, TITLE = {Braid group symmetries of {G}rassmannian cluster algebras}, JOURNAL = {Selecta Math. (N.S.)}, FJOURNAL = {Selecta Mathematica. New Series}, VOLUME = {26}, YEAR = {2020}, NUMBER = {2}, PAGES = {Paper No. 17, 51}, MRCLASS = {13F60 (14M15)}, MRNUMBER = {4066538}, MRREVIEWER = {Fan Qin}, DOI = {10.1007/s00029-020-0542-3}, URL = {https://doi.org/10.1007/s00029-020-0542-3}, } @article {karpwilliams, AUTHOR = {Karp, Steven N. and Williams, Lauren K.}, TITLE = {The {$m=1$} amplituhedron and cyclic hyperplane arrangements}, JOURNAL = {Int. Math. Res. Not. IMRN}, FJOURNAL = {International Mathematics Research Notices. IMRN}, YEAR = {2019}, volume = {5}, PAGES = {1401--1462}, MRCLASS = {14M15 (15B48 52B12 52B20 52C35)}, MRNUMBER = {3920352}, MRREVIEWER = {Felipe Zald\'{\i}var}, DOI = {10.1093/imrn/rnx140}, URL = {https://doi.org/10.1093/imrn/rnx140}, } @article {GLS, AUTHOR = {Geiss, Christof and Leclerc, Bernard and Schr\"{o}er, Jan}, TITLE = {Factorial cluster algebras}, JOURNAL = {Doc. Math.}, FJOURNAL = {Documenta Mathematica}, VOLUME = {18}, YEAR = {2013}, PAGES = {249--274}, MRCLASS = {13F60 (13F15)}, MRNUMBER = {3064982}, MRREVIEWER = {Li Li}, URL = {DOI removed}, } @article{karp2020decompositions, AUTHOR = {Karp, Steven N. and Williams, Lauren K. and Zhang, Yan X.}, TITLE = {Decompositions of amplituhedra}, NOTE = {With an appendix by Karp, Williams, Zhang and Hugh Thomas}, JOURNAL = {Ann. Inst. Henri Poincar\'e{} D}, FJOURNAL = {Annales de l'Institut Henri Poincar\'e{} D. Combinatorics, Physics and their Interactions}, VOLUME = {7}, YEAR = {2020}, NUMBER = {3}, PAGES = {303--363}, DOI = {10.4171/AIHPD/87}, URL = {https://doi.org/10.4171/AIHPD/87}, } @article{lam2015totally, title={Totally nonnegative Grassmannian and Grassmann polytopes}, author={Lam, Thomas}, journal={arXiv preprint arXiv:1506.00603}, year={2015} } @unpublished {FWZ, AUTHOR = {Sergey Fomin and Lauren Williams and Andrei Zelevinsky}, TITLE = {Introduction to cluster algebras: Chapters 1-3}, note={arXiv:1608.05735 [math.CO]}, eprint={1608.05735} } @unpublished {FWZ4, AUTHOR = {Sergey Fomin and Lauren Williams and Andrei Zelevinsky}, TITLE = {Introduction to cluster algebras: Chapters 4-5}, note={arXiv:1707.07190 [math.CO]}, eprint={1707.07190} } @unpublished {FWZ7, AUTHOR = {Sergey Fomin and Lauren Williams and Andrei Zelevinsky}, TITLE = {Introduction to cluster algebras: Chapter 7}, note={arXiv:2106.02160 [math.CO]}, eprint={2106.02160} } @article{Galashin_Lam_2020, title={Parity duality for the amplituhedron}, volume={156}, DOI={10.1112/S0010437X20007411}, number={11}, journal={Compos. Math.}, author={Galashin, Pavel and Lam, Thomas}, year={2020}, pages={2207-–2262} } @article {PSW, AUTHOR = {Parisi, Matteo and Sherman-Bennett, Melissa and Williams, Lauren K.}, TITLE = {The {$m=2$} amplituhedron and the hypersimplex: signs, clusters, tilings, {E}ulerian numbers}, JOURNAL = {Comm. Amer. Math. Soc.}, FJOURNAL = {Communications of the American Mathematical Society}, VOLUME = {3}, YEAR = {2023}, PAGES = {329--399}, MRCLASS = {13F60 (05E99 14M15 52B40 52C22)}, MRNUMBER = {4612722}, DOI = {10.1090/cams/23}, URL = {https://doi.org/10.1090/cams/23}, } @unpublished {FW6, AUTHOR = {Sergey Fomin and Lauren Williams and Andrei Zelevinsky}, TITLE = {Introduction to cluster algebras: Chapter 6}, note={arXiv:2008.09189 [math.CO]}, eprint={2008.09189} } @unpublished {FW7, AUTHOR = {Sergey Fomin and Lauren Williams and Andrei Zelevinsky}, TITLE = {Introduction to cluster algebras: Chapter 7}, note={arXiv:2106.02160 [math.CO]}, eprint={2106.02160} } @incollection {lusztig, AUTHOR = {Lusztig, G.}, TITLE = {Total positivity in reductive groups}, BOOKTITLE = {Lie theory and geometry}, SERIES = {Progr. Math.}, VOLUME = {123}, PAGES = {531--568}, PUBLISHER = {Birkh\"auser Boston, Boston, MA}, YEAR = {1994}, DOI = {10.1007/978-1-4612-0261-5\_20}, } @book{abcgpt, AUTHOR = {Arkani-Hamed, Nima and Bourjaily, Jacob and Cachazo, Freddy and Goncharov, Alexander and Postnikov, Alexander and Trnka, Jaroslav}, TITLE = {Grassmannian geometry of scattering amplitudes}, PUBLISHER = {Cambridge University Press, Cambridge}, YEAR = {2016}, PAGES = {ix+194 pp.}, MRCLASS = {81-02 (81R05 81R10 81T60)}, MRNUMBER = {3467729}, MRREVIEWER = {Yasuhiro Abe}, DOI = {10.1017/CBO9781316091548}, URL = {https://doi.org/10.1017/CBO9781316091548}, } @article {KLS, AUTHOR = {Knutson, Allen and Lam, Thomas and Speyer, David E.}, TITLE = {Positroid varieties: juggling and geometry}, JOURNAL = {Compos. Math.}, FJOURNAL = {Compositio Mathematica}, VOLUME = {149}, YEAR = {2013}, NUMBER = {10}, PAGES = {1710--1752}, MRCLASS = {14M15 (05B35 05E05)}, MRNUMBER = {3123307}, MRREVIEWER = {Jacopo Gandini}, URL = {https://doi.org/10.1112/S0010437X13007240}, } @article {postnikov, Author = {Alexander Postnikov}, Title = {Total positivity, {G}rassmannians, and networks}, Year = {2006}, Eprint = {math/0609764}, eprinttype = {arXiv}, } @article {arkani-hamed_trnka, AUTHOR = {Arkani-Hamed, Nima and Trnka, Jaroslav}, TITLE = {The Amplituhedron}, JOURNAL = {J. High Energy Phys.}, FJOURNAL = {Journal of High Energy Physics}, VOLUME = {2014}, NUMBER = {10}, PAGES = {33 pp.}, YEAR = {2014}, DOI = {10.1007/JHEP10(2014)030} } @article {bayer_93, AUTHOR = {Bayer, Margaret M.}, TITLE = {Equidecomposable and weakly neighborly polytopes}, JOURNAL = {Israel J. Math.}, FJOURNAL = {Israel Journal of Mathematics}, VOLUME = {81}, YEAR = {1993}, NUMBER = {3}, PAGES = {301--320}, MRCLASS = {52B35 (52B05)}, MRNUMBER = {1231196}, DOI = {10.1007/BF02764835}, URL = {http://dx.doi.org/10.1007/BF02764835}, } @article {rambau_97, AUTHOR = {Rambau, J{\"o}rg}, TITLE = {Triangulations of cyclic polytopes and higher {B}ruhat orders}, JOURNAL = {Mathematika}, FJOURNAL = {Mathematika. A Journal of Pure and Applied Mathematics}, VOLUME = {44}, YEAR = {1997}, NUMBER = {1}, PAGES = {162--194}, CODEN = {MTKAAB}, MRCLASS = {52B70 (52B05 52B12 57Q15)}, MRNUMBER = {1464385 (98i:52019)}, MRREVIEWER = {Jes{\'u}s A. de Loera}, DOI = {10.1112/S0025579300012055}, URL = {http://dx.doi.org/10.1112/S0025579300012055}, } @article{Arkani-Hamed:2010zjl, author = "Arkani-Hamed, Nima and Bourjaily, Jacob L. and Cachazo, Freddy and Caron-Huot, Simon and Trnka, Jaroslav", title = "{The All-Loop Integrand For Scattering Amplitudes in Planar N=4 SYM}", eprint = "1008.2958", archivePrefix = "arXiv", primaryClass = "hep-th", doi = "10.1007/JHEP01(2011)041", journal = "JHEP", volume = "01", pages = "041", year = "2011" } @article{Golden:2013xva, author = "Golden, John and Goncharov, Alexander B. and Spradlin, Marcus and Vergu, Cristian and Volovich, Anastasia", title = "{Motivic Amplitudes and Cluster Coordinates}", eprint = "1305.1617", archivePrefix = "arXiv", primaryClass = "hep-th", doi = "10.1007/JHEP01(2014)091", journal = "JHEP", volume = "01", pages = "091", year = "2014" } @article {Gurdougan2020ClusterPI, AUTHOR = {G\"{u}rdo\u{g}an, \"{O}mer and Parisi, Matteo}, TITLE = {Cluster patterns in {L}andau and leading singularities via the amplituhedron}, JOURNAL = {Ann. Inst. Henri Poincar\'{e} D}, FJOURNAL = {Annales de l'Institut Henri Poincar\'{e} D. Combinatorics, Physics and their Interactions}, VOLUME = {10}, YEAR = {2023}, NUMBER = {2}, PAGES = {299--336}, MRCLASS = {70S15 (13F60)}, MRNUMBER = {4581445}, MRREVIEWER = {Vladimir\ Dzhunushaliev}, DOI = {10.4171/aihpd/155}, URL = {https://doi.org/10.4171/aihpd/155}, } @article{Mago:2020kmp, author = "Mago, Jorge and Schreiber, Anders and Spradlin, Marcus and Volovich, Anastasia", title = "{Symbol alphabets from plabic graphs}", eprint = "2007.00646", archivePrefix = "arXiv", primaryClass = "hep-th", doi = "10.1007/JHEP10(2020)128", journal = "JHEP", volume = "10", pages = "128", year = "2020" } @article{He:2020uhb, author = "He, Song and Li, Zhenjie", title = "{A note on letters of Yangian invariants}", eprint = "2007.01574", archivePrefix = "arXiv", primaryClass = "hep-th", doi = "10.1007/JHEP02(2021)155", journal = "JHEP", volume = "02", pages = "155", year = "2021" } @article{Bourjaily:2010wh, author = "Bourjaily, Jacob L.", title = "{Efficient Tree-Amplitudes in N=4: Automatic BCFW Recursion in Mathematica}", eprint = "1011.2447", archivePrefix = "arXiv", primaryClass = "hep-ph", month = "11", year = "2010" } @article{Bai:2014cna, author = "Bai, Yuntao and He, Song", title = "{The Amplituhedron from Momentum Twistor Diagrams}", eprint = "1408.2459", archivePrefix = "arXiv", primaryClass = "hep-th", doi = "10.1007/JHEP02(2015)065", journal = "JHEP", volume = "02", pages = "065", year = "2015" } @article{Cresson, author = {Cresson, Jacky}, title = {Calculation {Moulien}}, journal = {Annals of the Faculty of Sciences of Toulouse: Mathematics}, pages = {307--395}, publisher = {Paul Sabatier University, Institute of Mathematics}, address = {Toulouse}, volume = {6th series, 18}, number = {2}, year = {2009}, doi = {10.5802/afst.1208}, mrnumber = {2562831}, language = {fr}, url = {http://www.numdam.org/articles/10.5802/afst.1208/} } @article{Basso:2023bwv, author = "Basso, Benjamin and Tumanov, Alexander G.", title = "{Wilson Loop Duality and OPE for Super Form Factors of Half-BPS Operators}", journal = "arXiv:2308.08432", primaryClass = "hep-th", year = "2023" } @article{Caron-Huot:2023wdh, author = {Caron-Huot, Simon and Coronado, Frank and M\"uhlmann, Beatrix}, title = "{Determinants in self-dual $ \mathcal{N} $ = 4 SYM and twistor space}", note = "\texttt{arXiv:2304.12341}", archivePrefix = "arXiv", primaryClass = "hep-th", doi = "10.1007/JHEP08(2023)008", journal = "JHEP", volume = "08", pages = "008", year = "2023" } @article{Kojima:2020tjf, author = "Kojima, Ryota and Langer, Cameron", title = "{Sign Flip Triangulations of the Amplituhedron}", eprint = "2001.06473", archivePrefix = "arXiv", primaryClass = "hep-th", reportNumber = "KEK-TH-2177", doi = "10.1007/JHEP05(2020)121", journal = "JHEP", volume = "05", pages = "121", year = "2020" } @article{He:2023rou, author = "He, Song and Huang, Yu-tin and Kuo, Chia-Kai", title = "{The ABJM Amplituhedron}", eprint = "2306.00951", archivePrefix = "arXiv", primaryClass = "hep-th", doi = "10.1007/JHEP09(2023)165", journal = "JHEP", volume = "09", pages = "165", year = "2023" } @article{Ferro:2023qdp, author = "Ferro, Livia and Glew, Ross and {\L}ukowski, Tomasz and Stalknecht, Jonah", title = "{Prescriptive Unitarity from Positive Geometries}", eprint = "2308.02438", archivePrefix = "arXiv", primaryClass = "hep-th", month = "8", year = "2023" } @article{Arkani-Hamed:2017tmz, author = "Arkani-Hamed, Nima and Bai, Yuntao and Lam, Thomas", title = "{Positive Geometries and Canonical Forms}", eprint = "1703.04541", archivePrefix = "arXiv", primaryClass = "hep-th", doi = "10.1007/JHEP11(2017)039", journal = "JHEP", volume = "11", pages = "039", year = "2017" } @article{Lam:2022yly, author = "Lam, Thomas", title = "{An invitation to positive geometries}", journal = "\emph{\texttt{arXiv:2208.05407}}", archivePrefix = "arXiv", primaryClass = "math.CO", year = "2022" } @article{LPW, AUTHOR = {\L ukowski, Tomasz and Parisi, Matteo and Williams, Lauren K.}, TITLE = {The positive tropical {G}rassmannian, the hypersimplex, and the {$m=2$} amplituhedron}, JOURNAL = {Int. Math. Res. Not. IMRN}, FJOURNAL = {International Mathematics Research Notices. IMRN}, YEAR = {2023}, NUMBER = {19}, PAGES = {16778--16836}, DOI = {10.1093/imrn/rnad010}, URL = {https://doi.org/10.1093/imrn/rnad010}, } @article {MullerSpeyerTwist, AUTHOR = {Muller, Greg and Speyer, David E.}, TITLE = {The twist for positroid varieties}, JOURNAL = {Proc. Lond. Math. Soc. (3)}, FJOURNAL = {Proceedings of the London Mathematical Society. Third Series}, VOLUME = {115}, YEAR = {2017}, NUMBER = {5}, PAGES = {1014--1071}, MRCLASS = {14M15 (05C22 13F60)}, MRNUMBER = {3733558}, MRREVIEWER = {Hoang\ Le\ Truong}, DOI = {10.1112/plms.12056}, URL = {https://doi.org/10.1112/plms.12056}, } @article {GalilMegiddo, AUTHOR = {Galil, Zvi and Megiddo, Nimrod}, TITLE = {Cyclic ordering is {NP}-complete}, JOURNAL = {Theoret. Comput. Sci.}, FJOURNAL = {Theoretical Computer Science}, VOLUME = {5}, YEAR = {1977/78}, NUMBER = {2}, PAGES = {179--182}, MRCLASS = {68C25}, MRNUMBER = {483648}, DOI = {10.1016/0304-3975(77)90005-6}, URL = {https://doi.org/10.1016/0304-3975(77)90005-6}, } @article {Meg_cyclicOrders, AUTHOR = {Megiddo, Nimrod}, TITLE = {Partial and complete cyclic orders}, JOURNAL = {Bull. Amer. Math. Soc.}, FJOURNAL = {Bulletin of the American Mathematical Society}, VOLUME = {82}, YEAR = {1976}, NUMBER = {2}, PAGES = {274--276}, DOI = {10.1090/S0002-9904-1976-14020-7}, URL = {https://doi.org/10.1090/S0002-9904-1976-14020-7}, } @article {AJR_cyclicOrders, AUTHOR = {Ayyer, Arvind and Josuat-Verg\`es, Matthieu and Ramassamy, Sanjay}, TITLE = {Extensions of partial cyclic orders and consecutive coordinate polytopes}, JOURNAL = {Ann. H. Lebesgue}, FJOURNAL = {Annales Henri Lebesgue}, VOLUME = {3}, YEAR = {2020}, PAGES = {275--297}, MRCLASS = {52B05 (05A05 05A10 06A75 52B11)}, MRNUMBER = {4113648}, MRREVIEWER = {Lionel\ Pournin}, DOI = {10.5802/ahl.33}, URL = {https://doi.org/10.5802/ahl.33}, } @article {PSWv1, AUTHOR = {Postnikov, Alexander and Speyer, David and Williams, Lauren}, TITLE = {Matching polytopes, toric geometry, and the totally non-negative {G}rassmannian}, JOURNAL = {J. Algebraic Combin.}, FJOURNAL = {Journal of Algebraic Combinatorics. An International Journal}, VOLUME = {30}, YEAR = {2009}, NUMBER = {2}, PAGES = {173--191}, DOI = {10.1007/s10801-008-0160-1}, } @article{Ranestad:2024svp, author = "Ranestad, Kristian and Sinn, Rainer and Telen, Simon", title = "{Adjoints and Canonical Forms of Tree Amplituhedra}", journal = "\emph{\texttt{arXiv:2402.06527}}", year = "2024" } @article{PSBTW, title={The Magic Number Conjecture for the $m=2$ amplituhedron and Parke-Taylor identities}, author={Matteo Parisi and Melissa Sherman-Bennett and Ran Tessler and Lauren Williams}, year={2024}, eprinttype = {arXiv}, eprint = {2404.03026}, }