$P$-Schur positive $P$-Grothendieck Polynomials

Abstract

The symmetric Grothendieck polynomials generalize Schur polynomials and are Schur-positive by degree. Combinatorially this is manifested as the generalization of semistandard Young tableaux by set-valued tableaux. We define a (weak) symmetric $P$-Grothendieck polynomial which generalizes $P$-Schur polynomials in the same way. Combinatorially this is manifested as the generalization of shifted semistandard Young tableaux by a new type of tableaux which we call shifted multiset tableaux.

References in corpus (2)

• $\mathfrak{q}$-crystal structure on primed tableaux and on signed unimodal factorizations of reduced words of type $B$
• Crystal structures for canonical Grothendieck functions