Related papers: RC-graphs and a generalized Littlewood-Richardson …
Given an rc-graph $R$ of permutation $w$ and an rc-graph $Y$ of permutation $v$, we provide an insertion algorithm, which defines an rc-graph $R\leftarrow Y$ in the case when $v$ is a shuffle with the descent at $r$ and $w$ has no descents…
We provide a generalization of the Schensted insertion algorithm for rc-graphs of Bergeron and Billey. The new algorithm is used to give a new proof of Pieri's formula.
For a given skew shape, we build a crystal graph on the set of all reverse plane partitions that have this shape. As a consequence, we get a simple extension of the Littlewood-Richardson rule for the expansion of the corresponding dual…
Notes from a course at the ATM Workshop on Schubert Varieties, held at The Institute of Mathematical Sciences, Chennai, in November 2017. Various expansions of Schur functions, the Lindstr\"om-Gessel-Viennot lemma, semistandard Young…
We introduce an insertion algorithm on Kohnert's combinatorial model for Demazure characters, generalizing Robinson--Schensted--Knuth insertion on tableaux. Our new insertion yields an explicit, nonnegative formula expressing the product of…
We generalize the Robinson-Schensted-Knuth algorithm to the insertion of two row arrays of multisets. This generalization leads to new enumerative results that have representation theoretic interpretations as decompositions of centralizer…
We give a Littlewood-Richardson type rule for expanding the product of a row-strict quasisymmetric Schur function and a symmetric Schur function in terms of row-strict quasisymmetric Schur functions. This expansion follows from several new…
We provide several ingredients towards a generalization of the Littlewood-Richardson rule from Chow groups to algebraic cobordism. In particular, we prove a simple product-formula for multiplying classes of smooth Schubert varieties with…
Schubert polynomials were introduced in the context of the geometry of flag varieties. This paper investigates some of the connections not yet understood between several combinatorial structures for the construction of Schubert polynomials;…
Schubert polynomials were discovered by A. Lascoux and M. Sch\"utzenberger in the study of cohomology rings of flag manifolds in 1980's. These polynomials generalize Schur polynomials, and form a linear basis of multivariate polynomials. In…
We prove a formula for double Schubert and Grothendieck polynomials specialized to two rearrangements of the same set of variables. Our formula generalizes the usual formulas for Schubert and Grothendieck polynomials in terms of RC-graphs,…
Following the methods used by Derksen-Weyman in \cite{DW11} and Chindris in \cite{Chi08}, we use quiver theory to represent the generalized Littlewood-Richardson coefficients for the branching rule for the diagonal embedding of $\gl(n)$ as…
In this paper, we study Grothendieck polynomials from a combinatorial viewpoint. We introduce the factorial Grothendieck polynomials, analogues of the factorial Schur functions and present some of their properties, and use them to produce a…
We present a partial generalization to Schubert calculus on flag varieties of the classical Littlewood-Richardson rule, in its version based on Schuetzenberger's jeu de taquin. More precisely, we describe certain structure constants…
We give a new formula for the Littlewood--Richardson coefficients in terms of peelable tableaux compatible with shuffle tableaux, in the same fashion as Remmel--Whitney rule. This gives an efficient way to compute generalized…
The classical Littlewood-Richardson rule is a rule for computing coefficients in many areas, and comes in many guises. In this paper we prove two Littlewood-Richardson rules for symmetric skew quasisymmetric Schur functions that are…
We develop the Littlewood-Richardson homotopy algorithm, which uses numerical continuation to compute solutions to Schubert problems on Grassmannians and is based on the geometric Littlewood-Richardson rule. One key ingredient of this…
We give a combinatorial rule for calculating the coefficients in the expansion of a product of two factorial Schur functions. It is a special case of a more general rule which also gives the coefficients in the expansion of a skew factorial…
Young's lattice, the lattice of all Young diagrams, has the Robinson-Schensted-Knuth correspondence, the correspondence between certain matrices and pairs of semi-standard Young tableaux with the same shape. Fomin introduced generalized…
We show that normalized Schur polynomials are strongly log-concave. As a consequence, we obtain Okounkov's log-concavity conjecture for Littlewood-Richardson coefficients in the special case of Kostka numbers.