TRANSITION ON GROTHENDIECK POLYNOMIALS

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A jeu de taquin theory for increasing tableaux, with applications to K-theoretic Schubert calculus (2007, methodology): “Other formulas for both Gπ and Gλ are also available; see, for example, [Buch et al. 2008; Knutson and Yong 2004; Knutson et al. 2008; Lascoux 2001] and the references therein.”
K-theory of minuscule varieties (2013, background): “The polynomials (−1)ℓ(w)Gw(−x1, . . . ,−xn−1) were introduced by Lascoux and Schützenberger as representatives for the Schubert classes in the K-theory of the flag manifold Fℓ(Cn) [19], and stabilizations of these polynomials were studied by Fomin and Kirillov in [11].”
Grothendieck classes of quiver varieties (2001, background): “Combined with some recent results of Lascoux [18], this supplies additional evidence for our conjecture about the signs of the coefficients cμ(r).”
Newton polytopes in algebraic combinatorics (2017, background): “wton(S w) = Newton(G w) \ ( ( 1;:::; n) 2Rn: Xn i=1 i= #D w ) : Grothendieck polynomials arise in combinatorial K-theory. Another family of polynomials from this topic was introduced by A. Lascoux in [La00]. He deﬁnes for = ( 1 1; 2;:::) 2Z 0 by replacing ˇ iin the deﬁnition of with ˝ i(f) = @ i(x ”