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Pechenik, Speyer and Weigandt defined a statistic rajcode(⋅) 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.
Chou et al. (Thu,) studied this question.