We define an action of the symmetric group S[ n 2 ] on the set of domino tableaux, and prove that the number of domino tableaux of weight β does not depend on the permutation of the weight β. A bijective proof of the well-known result due to J. Stembridge that the number of self–evacuating tableaux of a given shape and weight β = (β1, . . . , β[ n+1 2 ], β[ n2 ], . . . , β1), is equal to that o...

We introduce a mutation algorithm for puzzles that is a threedirection analogue of the classical jeu de taquin algorithm for semistandard tableaux. We apply this algorithm to prove our conjectured puzzle formula for the equivariant Schubert structure constants of two-step flag varieties. This formula gives an expression for the structure constants that is positive in the sense of Graham. Thanks...

A key fact about M.-P. Schützenberger’s (1972) promotion operator on rectangular standard Young tableaux is that iterating promotion once per entry recovers the original tableau. For tableaux with strictly increasing rows and columns, H. Thomas and A. Yong (2009) introduced a theory of K-jeu de taquin with applications to K-theoretic Schubert calculus. The author (2014) studied a K-promotion op...

We define an action of the symmetric group S[ n 2 ] on the set of domino tableaux, and prove that the number of domino tableaux of weight β does not depend on the permutation of the weight β. A bijective proof of the well-known result due to J. Stembridge that the number of self–evacuating tableaux of a given shape and weight β = (β1, . . . , β[ n+1 2 ], β[ n2 ], . . . , β1), is equal to that o...

We prove a root system uniform, concise combinatorial rule for Schubert calculus of minuscule and cominuscule flag manifolds G/P (the latter are also known as compact Hermitian symmetric spaces). We connect this geometry to the poset combinatorics of [Proc-tor '04], thereby giving a generalization of the [Schützenberger '77] jeu de taquin formulation of the Littlewood-Richardson rule that compu...

We present a new bijective proof of the equality between the number of Littlewood-Richardson fillings of a skew-shape i/n of weight v, and those of the conjugate skew-shape A’/$, of conjugate weight v’. The bijection is defined by means of a unique permutation a,,, associated to the skew-shape i-/p. Our arguments use only well-established properties of Schensted insertion, and make no reference...

We prove a root system uniform, concise combinatorial rule for Schubert calculus of minuscule and cominuscule flag manifolds G/P (the latter are also known as compact Hermitian symmetric spaces). We connect this geometry to the poset combinatorics of [Proc-tor '04], thereby giving a generalization of the [Schützenberger '77] jeu de taquin formulation of the Littlewood-Richardson rule that compu...