Related papers: A closed formula of Littlewood-Richardson coeffici…
Littlewood Richardson coefficients are structure constants appearing in the representation theory of the general linear groups ($GL_n$). The main results of this paper are: 1. A strongly polynomial randomized approximation scheme for…
We show that the Littlewood-Richardson coefficients are values at 1 of certain parabolic Kazhdan-Lusztig polynomials for affine symmetric groups. These q-analogues of Littlewood-Richardson multiplicities coincide with those previously…
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…
The reduced Schur functions are studied. Their relations to the basic representation of $A^(1)_{r-1}$ and modular representations of the symmetric groups are clarified. Littlewood-Richardson coefficients appear in the linear relations among…
We define and study a generalization of the Littlewood-Richardson (LR) coefficients, which we call the flagged skew LR coefficients. These subsume several previously studied extensions of the LR coefficients. We establish the saturation…
We give a survey on the Littlewood-Richardson rule. Using Gelfand-Tsetlin patterns as the main machinery of our analysis, we study the interrelationship of various combinatorial descriptions of the Littlewood-Richardson rule.
The Littlewood-Richardson coefficients describe the decomposition of tensor products of irreducible representations of a simple Lie algebra into irreducibles. Assuming the number of factors is large, one gets a measure on the space of…
Littlewood-Richardson (LR) coefficients and Kostka Numbers appear in representation theory and combinatorics related to $GL_n$. It is known that Kostka numbers can be represented as special Littlewood-Rischardson coefficient. In this paper,…
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…
An introduction is given to the Littlewood-Richardson rule, and various combinatorial constructions related to it. We present a proof based on tableau switching, dual equivalence, and coplactic operations. We conclude with a section…
We study the Littlewood-Richardson coefficients of double Grothendieck polynomials indexed by Grassmannian permutations. Geometrically, these are the structure constants of the equivariant $K$-theory ring of Grassmannians. Representing the…
This note has a twofold purpose. To improve the best known lower estimates of the Hardy-Littlewood inequality for $m$-linear forms in $\ell_{p}$ spaces and to provide a closed formula encompassing the cases $p>2m$ and $% p=2m.$ Our approach…
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…
We introduce a family of rings of symmetric functions depending on an infinite sequence of parameters. A distinguished basis of such a ring is comprised by analogues of the Schur functions. The corresponding structure coefficients are…
We give counterexamples to Okounkov's log-concavity conjecture for Littlewood-Richardson coefficients.
We provide direct proofs of product and coproduct formulae for Schur functions where the coefficients (Littlewood--Richardson coefficients) are defined as counting puzzles. The product formula includes a second alphabet for the Schur…
The Littlewood-Richardson (LR) coefficient counts among many other things the LR tableaux of a given shape and a given content. We prove, that the number of LR tableaux weakly increases if one adds to the shape and the content the shape and…
We derive an integral representation which encodes all coefficients of the Riemann normal coordinate expansion, and also a closed formula for those coefficients.
We relate noncommutative Littlewood-Richardson coefficients of Bessenrodt-Luoto-van Willigenburg to classical Littlewood-Richardson coefficients via crystal reflection operators. A key role is played by the combinatorics of frank words.
We find and prove a factorization formula for certain Macdonald Littlewood-Richardson coefficients $c_{\lambda\mu}^{\nu}(q,t)$. Namely, we consider the case that the Kostka number $K_{\mu, \nu -\lambda}$ is $1$. This settles a particular…