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Hawkes, Graham 1 ; Scrimshaw, Travis 2
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@article{ALCO_2020__3_3_727_0,
author = {Hawkes, Graham and Scrimshaw, Travis},
title = {Crystal structures for canonical {Grothendieck} functions},
journal = {Algebraic Combinatorics},
pages = {727--755},
publisher = {MathOA foundation},
volume = {3},
number = {3},
year = {2020},
doi = {10.5802/alco.111},
mrnumber = {4113604},
zbl = {1441.05236},
language = {en},
url = {https://geodesic-test.mathdoc.fr/articles/10.5802/alco.111/}
}
TY - JOUR AU - Hawkes, Graham AU - Scrimshaw, Travis TI - Crystal structures for canonical Grothendieck functions JO - Algebraic Combinatorics PY - 2020 SP - 727 EP - 755 VL - 3 IS - 3 PB - MathOA foundation UR - https://geodesic-test.mathdoc.fr/articles/10.5802/alco.111/ DO - 10.5802/alco.111 LA - en ID - ALCO_2020__3_3_727_0 ER -
%0 Journal Article %A Hawkes, Graham %A Scrimshaw, Travis %T Crystal structures for canonical Grothendieck functions %J Algebraic Combinatorics %D 2020 %P 727-755 %V 3 %N 3 %I MathOA foundation %U https://geodesic-test.mathdoc.fr/articles/10.5802/alco.111/ %R 10.5802/alco.111 %G en %F ALCO_2020__3_3_727_0
Hawkes, Graham; Scrimshaw, Travis. Crystal structures for canonical Grothendieck functions. Algebraic Combinatorics, Tome 3 (2020) no. 3, pp. 727-755. doi : 10.5802/alco.111. https://geodesic-test.mathdoc.fr/articles/10.5802/alco.111/
[1] Combinatorial expansions in
[2] A minimaj-preserving crystal on ordered multiset partitions, Adv. in Appl. Math., Volume 95 (2018), pp. 96-115 | Zbl | MR | DOI
[3] A Littlewood–Richardson rule for the
[4] Stable Grothendieck polynomials and
[5]
[6] Crystal bases: Representations and Combinatorics, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2017, xii+279 pages | Zbl | MR | DOI
[7] Grothendieck polynomials and the Yang–Baxter equation, Formal Power Series and Algebraic Combinatorics/Séries Formelles et Combinatoire Algébrique, DIMACS, Piscataway, NJ, 1994, pp. 183-189 | MR
[8] The Yang–Baxter equation, symmetric functions, and Schubert polynomials, Discrete Math., Volume 153 (1996) no. 1-3, pp. 123-143 | Zbl | MR | DOI
[9]
[10] A Littlewood–Richardson rule for dual stable Grothendieck polynomials, J. Combin. Theory Ser. A, Volume 151 (2017), pp. 23-35 | Zbl | MR | DOI
[11] A Thom–Porteous formula for connective
[12] Peterson isomorphism in
[13] Excited Young diagrams and equivariant Schubert calculus, Trans. Amer. Math. Soc., Volume 361 (2009) no. 10, pp. 5193-5221 | Zbl | MR | DOI
[14] A proof of
[15] Grothendieck polynomials and the boson-fermion correspondence (2019) (Preprint, https://arxiv.org/abs/1905.07692)
[16] Crystalizing the
[17] On crystal bases of the
[18] The crystal base and Littelmann’s refined Demazure character formula, Duke Math. J., Volume 71 (1993) no. 3, pp. 839-858 | Zbl | MR | DOI
[19] Combinatorial Hopf algebras and
[20] The Plactic Monoid, Algebraic Combinatorics on Words (Lothaire, M., ed.), Cambridge University Press, Cambridge, 2002
[21] Structure de Hopf de l’anneau de cohomologie et de l’anneau de Grothendieck d’une variété de drapeaux, C. R. Acad. Sci. Paris Sér. I Math., Volume 295 (1982) no. 11, pp. 629-633 | Zbl | MR
[22] Symmetry and flag manifolds, Invariant theory (Montecatini, 1982) (Lecture Notes in Math.), Volume 996, Springer, Berlin, 1983, pp. 118-144 | Zbl | MR | DOI
[23] Combinatorial aspects of the
[24] On the combinatorics of crystal graphs. I. Lusztig’s involution, Adv. Math., Volume 211 (2007) no. 1, pp. 204-243 | Zbl | MR | DOI
[25] Générateurs et relations des groupes de Weyl généralisés, C. R. Acad. Sci. Paris, Volume 258 (1964), pp. 3419-3422 | Zbl | MR
[26] Set-valued skyline fillings (2016) (Preprint, http://arxiv.org/abs/1611.08777)
[27] Crystal structures for symmetric Grothendieck polynomials (2018) (Preprint, http://arxiv.org/abs/1807.03294)
[28] Polynomials from combinatorial
[29] Vertex models, TASEP and Grothendieck polynomials, J. Phys. A, Volume 46 (2013) no. 35, 355201, 26 pages | Zbl | MR | DOI
[30]
[31] Combinatorics of
[32] K-theoretic crystals for set-valued tableaux of rectangular shape (2019) (Preprint, http://arxiv.org/abs/1904.09674)
[33] Decompositions of Grothendieck polynomials, Int. Math. Res. Not. IMRN, Volume 2019 (2019) no. 10, pp. 3214-3241 | Zbl | MR | DOI
[34] Genomic tableaux, J. Algebraic Combin., Volume 45 (2017) no. 3, pp. 649-685 | MR | DOI | Zbl
[35] Puzzles in
[36] Poset edge densities, nearly reduced words, and barely set-valued tableaux, J. Combin. Theory Ser. A, Volume 158 (2018), pp. 66-125 | Zbl | MR | DOI
[37] Sage-Combinat: enhancing Sage as a toolbox for computer exploration in algebraic combinatorics, 2008 (https://wiki.sagemath.org/combinat)
[38] Sage Mathematics Software (Version 8.8), 2019 (https://www.sagemath.org)
[39] Enumerative combinatorics. Vol. 2, Cambridge Studies in Advanced Mathematics, 62, Cambridge University Press, Cambridge, 1999, xii+581 pages (With a foreword by Gian-Carlo Rota and appendix 1 by Sergey Fomin) | Zbl | MR | DOI
[40] A local characterization of simply-laced crystals, Trans. Amer. Math. Soc., Volume 355 (2003) no. 12, pp. 4807-4823 | Zbl | MR | DOI
[41] A jeu de taquin theory for increasing tableaux, with applications to
[42] Longest increasing subsequences, Plancherel-type measure and the Hecke insertion algorithm, Adv. in Appl. Math., Volume 46 (2011) no. 1-4, pp. 610-642 | Zbl | MR | DOI
[43] Littlewood–Richardson coefficients for Grothendieck polynomials from integrability, J. Reine Angew. Math., Volume 757 (2019), pp. 159-195 | Zbl | MR | DOI
[44] Duality and deformations of stable Grothendieck polynomials, J. Algebraic Combin., Volume 45 (2017) no. 1, pp. 295-344 | Zbl | MR | DOI
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