We use Hopf algebras to prove a version of the Littlewood–Richardson rule for skew Schur functions, which implies a conjecture of Assaf and McNamara. We also establish skew Littlewood–Richardson rules for Schur P and Q-functions and noncommutative ribbon Schur functions, as well as skew Pieri rules for k-Schur functions, dual k-Schur functions, and for the homology of the affine Grassmannian of...

This study investigates the sensitivity of the dynamics of the equatorial ocean to the parameterization of vertical mixing and focuses on the circulation in the meridionalvertical plane driven by easterly winds: the Yoshida jet. A new high resolution, numerical model of a zonally independent, equatorial channel helps explore this question and includes three parameterizations, all of which incre...

We present a multilevel algorithm to compute steady states of lattice Boltzmann models directly as fixed points of a time-stepper. At the fine scale, we use a Richardson iteration for the fixed point equation, which amounts to time-stepping towards equilibrium. This fine-scale iteration is accelerated by transferring the error to a coarse level. At this coarse level, one directly solves for the...

In this paper we investigate Q(n) = Q λ′,μ′ (n) = P ν c(nλ + λ;nμ+ μ, ν) as a function of n and show that Q(n) is bounded above if and only if λ/μ is a partition or rotated partition. Here c(λ;μ, ν) is the LittlewoodRichardson coefficient. So Q(n) counts the number of LR tableaux of shape (nλ + λ)/(nμ + μ) or the total number of irreducible characters in the skew character [(nλ+ λ)/(nμ + μ)]. W...

We describe an explicit geometric Littlewood-Richardson rule, interpreted as deforming the intersection of two Schubert varieties so that they break into Schubert varieties. There are no restrictions on the base field, and all multiplicities arising are 1; this is important for applications. This rule should be seen as a generalization of Pieri’s rule to arbitrary Schubert classes, by way of ex...

We introduce a Littlewood-Richardson rule based on an algorithmic deformation of skew Young diagrams and present a bijection with the classical rule. The result is a direct combinatorial interpretation and proof of the geometric rule presented by Coskun (2000). We also present a corollary regarding the Specht modules of the intermediate diagrams.