A bijection between \(K\)-Kohnert diagrams and reverse set-valued tableaux (Q6117244)

Summary: Lascoux polynomials are \(K\)-theoretic analogues of the key polynomials. They both have combinatorial formulas involving tableaux: reverse set-valued tableaux (\textsf{RSVT}) rule for Lascoux polynomials and reverse semistandard Young tableaux (\textsf{RSSYT}) rule for key polynomials. Furthermore, key polynomials have a simple algorithmic model in terms of Kohnert diagrams, which are in bijection with \textsf{RSSYT}. \textit{C. Ross} and \textit{A. Yong} [Sémin. Lothar. Comb. 74, B74a, 11 p. (2015; Zbl 1328.05200)] introduced \(K\)-Kohnert diagrams, which are analogues of Kohnert diagrams. They conjectured a \(K\)-Kohnert diagram rule for Lascoux polynomials. We establish this conjecture by constructing a weight-preserving bijection between \textsf{RSVT} and \(K\)-Kohnert diagrams.