Constructing Maximal Pipedreams of Double Grothendieck Polynomials

Pechenik, Speyer and Weigandt defined a statistic rajcode (<middle dot>) on permutations which characterizes the leading monomial in top degree components of double Grothendieck polynomials. Their proof is combinatorial: They showed there exists a unique pipedream of a permutation w with row weight rajcode (w) and column weight rajcode (w(-1)). They proposed the problem of finding a "direct recipe" for this pipedream. We solve this problem by providing an algorithm that constructs this pipedream via ladder moves.