On a bijection between Littlewood-Richardson fillings of conjugate shape (Q1186106)

The paper provides a direct bijective proof of the following fact (which is clear from a representation-theoretic point of view): the Littlewood- Richardson coefficients \(g_{\mu\nu}^{\lambda}\) satisfy the identity \(g_{\mu\nu}^{\lambda}=g_{\mu'\nu'}^{\lambda'}\) where \(\lambda'\) denoted the conjugate of the partition (shape) \(\lambda\). The construction is based on Schensted insertion. For related results, see \textit{A.V.Zelevinsky} [J.Algebra 69, 82-94 (1981; Zbl 0464.20010), Proposition 8]and \textit{S.Fomin} and \textit{C.Greene} [Institut Mittag- Leffler, Report No. 33 (1991/92), Corollary 7.7].