A row analogue of Hecke column insertion

We introduce a new row insertion algorithm on decreasing tableaux and increasing tableaux, generalizing Edelman-Greene (EG) row insertion. Our row insertion algorithm is a nontrivial variation of Hecke column insertion which generalizes EG column insertion. Similar to Hecke column insertion, our row insertion is bijective and respects Hecke equivalence, and therefore recovers the expansions of Grothendieck symmetric functions into Grassmannian Grothendieck functions. In future work, we will use this row insertion to establish an expansion of products between Lascoux polynomials and certain Grothendieck polynomials, which cannot be done by Hecke column insertion.