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@book{FK94,
  author    = {Fomin, S. and Kirillov, A.},
  booktitle = {Formal power series and algebraic combinatorics/{S}\'eries formelles et combinatoire alg\'ebrique},
  publisher = {DIMACS, Piscataway, NJ},
  title     = {Grothendieck polynomials and the {Y}ang-{B}axter equation},
  year      = {1994},
  pages     = {183--189},
  mrclass   = {05E05 (14N15)book},
  mrnumber  = {2307216},
}

@Article{LMS79,
  author     = {Lakshmibai, V. and Musili, C. and Seshadri, C. S.},
  title      = {Geometry of {$G/P$}. {IV}. {S}tandard monomial theory for classical types},
  issn       = {0370-0089},
  number     = {4},
  pages      = {279--362},
  volume     = {88},
  fjournal   = {Indian Academy of Sciences. Proceedings. Section A. Mathematical Sciences},
  journal    = {Proc. Indian Acad. Sci. Sect. A Math. Sci.},
  mrclass    = {14M15 (14L30 14M17)},
  mrnumber   = {553746},
  mrreviewer = {H. H. Andersen},
  year       = {1979},
}

@article{BSW19,
  author = {Buciumas, V. and Scrimshaw, T. and Weber, K.},
  title  = {Colored five-vertex models and {L}ascoux polynomials and atoms},
  journal={Journal of the London Mathematical Society},
doi={10.1112/jlms.12347},
  year   = {2020},
}


@Article{RY15,
  author     = {Ross, C. and Yong, A.},
  title      = {Combinatorial rules for three bases of polynomials},
  issn       = {1286-4889},
  pages      = {Art. B74a, 11},
  volume     = {74},
  fjournal   = {S\'eminaire Lotharingien de Combinatoire},
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  mrclass    = {05E05},
  mrnumber   = {3383158},
  mrreviewer = {Justin Mark Allman},
  year       = {2015},
}

@misc{BBBG19,
  author = {B. Brubaker and V. Buciumas and D. Bump and H. Gustafsson},
  title  = {Coloured five-vertex models and {D}emazure atoms},
 eprint={1902.01795},
  year   = {2019},
}

@misc{PS19,
  author = {Pechenik, O. and Scrimshaw, T.},
  title  = {K-theoretic crystals for set-valued tableaux of rectangular shapes},
  eprint={1904.09674},
  year   = {2019},
}

@Article{Andersen85,
  author     = {H. Andersen},
  title      = {Schubert varieties and {D}emazure's character formula},
  doi        = {10.1007/BF01388527},
  number     = {3},
  pages      = {611--618},
  volume     = {79},
  fjournal   = {Inventiones Mathematicae},
  journal    = {Invent. Math.},
  mrclass    = {14M15 (14F05 20G05)},
  mrnumber   = {782239},
  mrreviewer = {S. Ramanan},
  year       = {1985},
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@misc{MPS18,
  author = {Monical, C. and Pechenik, O. and Scrimshaw, T.},
  title  = {Crystal structures for symmetric {G}rothendieck polynomials},
  eprint={1807.03294},
  year   = {2018},
}

@Article{WZJ16,
  author   = {Wheeler, M. and Zinn-Justin, Paul},
  title    = {Littlewood-{R}ichardson coefficients for {G}rothendieck polynomials from integrability},
  doi      = {10.1515/crelle-2017-0033},
  fjournal = {Journal f\"{u}r die reine und angewandte Mathematik},
  journal  = {J. Reine Angew. Math.},
  volume = "2019",
      number = "757",
      pages=      "159 -- 195",
  year     = {2017},
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@Manual{sage,
  title        = {{S}age {M}athematics {S}oftware ({V}ersion 8.7)},
  note         = {\url{http://www.sagemath.org}},
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  key          = {Sage},
  year         = {2019},
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@Article{Kirillov:notes,
  author   = {Kirillov, A.},
  title    = {Notes on {S}chubert, {G}rothendieck and key polynomials},
  pages    = {Paper No. 034, 1--56},
  volume   = {12},
  fjournal = {SIGMA. Symmetry, Integrability and Geometry. Methods and Applications},
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  year     = {2016},
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@book{Lascoux01,
  author     = {Lascoux, A.},
  booktitle  = {Physics and combinatorics, 2000 ({N}agoya)},
  title      = {Transition on {G}rothendieck polynomials},
  doi        = {10.1142/9789812810007_0007},
  pages      = {164--179},
  publisher  = {World Sci. Publ., River Edge, NJ},
  mrclass    = {14M15 (05E05 19E08)},
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  mrreviewer = {Frank Sottile},
  year       = {2001},
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@Article{Willis13,
  author   = {Willis, Matthew J.},
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  doi      = {10.1007/s00026-013-0187-4},
  number   = {2},
  pages    = {393--400},
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  year     = {2013},
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@Book{LS83,
  author     = {Lascoux, A. and Sch{\"u}tzenberger, M.-P.},
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  title      = {Symmetry and flag manifolds},
  doi        = {10.1007/BFb0063238},
  pages      = {118--144},
  publisher  = {Springer, Berlin},
  series     = {Lecture Notes in Math.},
  volume     = {996},
  mrclass    = {14M17 (20B30 32M10)},
  mrnumber   = {718129},
  mrreviewer = {Konrad Drechsler},
  year       = {1983},
}

@Article{LS82,
  author   = {Lascoux, A. and Sch{\"u}tzenberger, M.-P.},
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  issn     = {0249-6321},
  number   = {11},
  pages    = {629--633},
  volume   = {295},
  coden    = {CHASAP},
  fjournal = {Comptes Rendus des S\'eances de l'Acad\'emie des Sciences. S\'erie I. Math\'ematique},
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  mrclass  = {14M17},
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  year     = {1982},
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@Book{Sagan01,
  author    = {Sagan, B. E.},
  title     = {The symmetric group},
  doi       = {10.1007/978-1-4757-6804-6},
  edition   = {Second},
  isbn      = {0-387-95067-2},
  note      = {Representations, combinatorial algorithms, and symmetric functions},
  pages     = {xvi+238},
  publisher = {Springer-Verlag, New York},
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  volume    = {203},
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  year      = {2001},
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@Article{K93,
  author     = {Kashiwara, M.},
  title      = {The crystal base and {L}ittelmann's refined {D}emazure character formula},
  doi        = {10.1215/S0012-7094-93-07131-1},
  issn       = {0012-7094},
  number     = {3},
  pages      = {839--858},
  volume     = {71},
  coden      = {DUMJAO},
  fjournal   = {Duke Mathematical Journal},
  journal    = {Duke Math. J.},
  mrclass    = {17B37 (17B10 17B67)},
  mrnumber   = {1240605 (95b:17019)},
  mrreviewer = {Kailash C. Misra},
  year       = {1993},
}

@misc{Monical16,
  author = {Monical, C.},
  title  = {Set-valued skyline fillings},
  eprint={1611.08777},
  year   = {2016},
}

@Article{Buch02,
  author     = {Buch, A.},
  title      = {A {L}ittlewood-{R}ichardson rule for the {$K$}-theory of {G}rassmannians},
  doi        = {10.1007/BF02392644},
  number     = {1},
  pages      = {37--78},
  volume     = {189},
  coden      = {ACMAA8},
  fjournal   = {Acta Mathematica},
  journal    = {Acta Math.},
  mrclass    = {14M15 (05E05 05E15)},
  mrnumber   = {1946917},
  mrreviewer = {Frank Sottile},
  year       = {2002},
}

@Article{IN13,
  author     = {Ikeda, T. and Naruse, H.},
  title      = {{$K$}-theoretic analogues of factorial {S}chur {$P$}- and {$Q$}-functions},
  doi        = {10.1016/j.aim.2013.04.014},
  issn       = {0001-8708},
  pages      = {22--66},
  volume     = {243},
  fjournal   = {Advances in Mathematics},
  journal    = {Adv. Math.},
  mrclass    = {05E05 (14M15 19L47)},
  mrnumber   = {3062739},
  mrreviewer = {Li Li},
  year       = {2013},
}

@Article{Mason08,
  author     = {Mason, S.},
  title      = {A decomposition of {S}chur functions and an analogue of the {R}obinson-{S}chensted-{K}nuth algorithm},
  issn       = {1286-4889},
  pages      = {Art. B57e, 24},
  volume     = {57},
  fjournal   = {S\'{e}minaire Lotharingien de Combinatoire},
  journal    = {S\'{e}m. Lothar. Combin.},
  mrclass    = {05E05 (05E10)},
  mrnumber   = {2461993},
  mrreviewer = {Grant Walker},
  year       = {2006/08},
}

@misc{BorodinWheelerColored,
  author     = {A. Borodin and M. Wheeler},
  title      = {Coloured stochastic vertex models and their spectral theory},
  eprint     = {1808.01866},
  eprinttype = {Arxiv},
  year       = {2018},
}

@Article{Mason09,
  author     = {Mason, S.},
  title      = {An explicit construction of type {A} {D}emazure atoms},
  doi        = {10.1007/s10801-008-0133-4},
  issn       = {0925-9899},
  number     = {3},
  pages      = {295--313},
  volume     = {29},
  fjournal   = {Journal of Algebraic Combinatorics. An International Journal},
  journal    = {J. Algebraic Combin.},
  mrclass    = {05E05 (05E10)},
  mrnumber   = {2496309},
  mrreviewer = {James B. Haglund},
  year       = {2009},
}

@Article{MS13,
  author   = {Motegi, K. and Sakai, K.},
  title    = {Vertex models, {TASEP} and {G}rothendieck polynomials},
  doi      = {10.1088/1751-8113/46/35/355201},
  issn     = {1751-8113},
  number   = {35},
  pages    = {355201, 26},
  volume   = {46},
  fjournal = {Journal of Physics. A. Mathematical and Theoretical},
  journal  = {J. Phys. A},
  mrclass  = {81R12},
  mrnumber = {3100873},
  year     = {2013},
}

@Article{MS14,
  author   = {Motegi, K. and Sakai, K.},
  title    = {{$K$}-theoretic boson-fermion correspondence and melting crystals},
  doi      = {10.1088/1751-8113/47/44/445202},
  number   = {44},
  pages    = {445202},
  volume   = {47},
  fjournal = {Journal of Physics. A. Mathematical and General},
  journal  = {J. Phys. A},
  year     = {2014},
}

@Article{IS14,
  author     = {Ikeda, T. and Shimazaki, T.},
  title      = {A proof of {$K$}-theoretic {L}ittlewood-{R}ichardson rules by {B}ender-{K}nuth-type involutions},
  doi        = {10.4310/MRL.2014.v21.n2.a10},
  issn       = {1073-2780},
  number     = {2},
  pages      = {333--339},
  volume     = {21},
  fjournal   = {Mathematical Research Letters},
  journal    = {Math. Res. Lett.},
  mrclass    = {05E05 (14M15 19E08)},
  mrnumber   = {3247060},
  mrreviewer = {M. Orin Joyce},
  year       = {2014},
}

@Article{Kuperberg96,
  author     = {Kuperberg, G.},
  title      = {Another proof of the alternating-sign matrix conjecture},
  doi        = {10.1155/S1073792896000128},
  issn       = {1073-7928},
  number     = {3},
  pages      = {139--150},
  fjournal   = {International Mathematics Research Notices},
  journal    = {Internat. Math. Res. Notices},
  mrclass    = {05A15 (33D45 82B23)},
  mrnumber   = {1383754},
  mrreviewer = {Jiang Zeng},
  year       = {1996},
}

@Article{MPS18II,
  author   = {Monical, Cara and Pechenik, Oliver and Searles, Dominic},
  title    = {Polynomials from combinatorial {$K$}-theory},
  doi      = {10.4153/S0008414X19000464},
  note     = {To appear},
  fjournal = {Canadian Journal of Mathematics},
  journal  = {Canad. J. Math.},
  year     = {2019},
}

@Comment{jabref-meta: databaseType:bibtex;}