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Lascoux polynomials are $K$-theoretic analogues of the key polynomials. Theyboth have combinatorial formulas involving tableaux: reverse set-valuedtableaux ($\mathsf{RSVT}$) rule for Lascoux polynomials and reversesemistandard Young tableaux ($\mathsf{RSSYT}$) rule for key polynomials.Furthermore, key polynomials have a simple algorithmic model in terms ofKohnert diagrams, which are in bijection with $\mathsf{RSSYT}$. Ross and Yongintroduced $K$-Kohnert diagrams, which are analogues of Kohnert diagrams. Theyconjectured a $K$-Kohnert diagram rule for Lascoux polynomials. We establishthis conjecture by constructing a weight-preserving bijection between$\mathsf{RSVT}$ and $K$-Kohnert diagrams.

A bijection between $K$-Kohnert diagrams and reverse set-valued tableaux