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1 de ago. de 2021 · Graham Hawkes. We give combinatorial proofs of two types of duality for Grothendieck polynomials by constructing a unified combinatorial framework incorporating set-valued tableaux, musltiset-valued tableaux, reverse plane partitions and valued-set tableaux.
GRAHAM HAWKES Abstract. We give a new proof of the generalized Cauchy identity for double Grothendieck polynomials, a combinatorial interpretation of the stable double Grothendieck polynomials in terms of triples of tableaux, and an interpolation between the stable double Grothendieck polynomial and the weak stable double Grothendieck polynomial.
Graham Hawkes; Published 1 August 2021; Mathematics. We give combinatorial proofs of two types of duality for Grothendieck polynomials by constructing a unified combinatorial framework incorporating set-valued tableaux, musltiset-valued tableaux, reverse plane partitions and valued-set tableaux.
GRAHAM HAWKES Abstract. We give new proofs of the two types of duality for Grothendieck polynomials. Our proofs extend to proofs of these dualities for the refined Grothendieck polynomials. The second of these dualities was unknown for the refined case. 1. Introduction The Grassmannian is the set of k-dimensional hyperplanes in Cn. Lascoux and
26 de jul. de 2019 · Graham Hawkes, Travis Scrimshaw. Published in Algebraic Combinatorics 26 July 2019. Mathematics. We give a $U_q (\mathfrak {sl}_n)$-crystal structure on multiset-valued tableaux, hook-valued tableaux, and valued-set tableaux, whose generating functions are the weak symmetric, canonical, and dual weak symmetric Grothendieck functions, respectively.
We give a self-contained treatment of double Grothendieck polynomials including many new combinatorial results such as a combinatorial proof of the $k$-theoretic ...
GRAHAM HAWKES Max-Planck-Institut fur Mathematik, Vivatsgasse 7, 53111 Bonn, Germany Abstract. The symmetric Grothendieck polynomials generalize Schur poly-nomials and are Schur-positive by degree. Combinatorially this is manifested as the generalization of semistandard Young tableaux by set-valued tableaux.
