For 1423-avoiding permutations, the principal specialization of β-Grothendieck polynomials is a nonnegative sum over pattern occurrence counts in the permutation, proved by reducing pipe dreams.
Zhang, Principal specializations of Schubert polynomials, multi-layered permutations and asymptotics, Adv
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Principal specializations of Grothendieck polynomials
For 1423-avoiding permutations, the principal specialization of β-Grothendieck polynomials is a nonnegative sum over pattern occurrence counts in the permutation, proved by reducing pipe dreams.