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...

The notion of pairing plays a central role in the BCS theory of superconductivity. In 1963, R.W. Richardson showed that exact energy eigenvalues and eigenstates of the BCS pairing Hamiltonian can be computed if one can solve a given set of highly coupled nonlinear equations. The limit of these equations in which the BCS coupling constant is very large were also obtained by Gaudin in 1976. Gaudi...

The present study investigates numerically the phenomenon of vortex-shedding and its suppression in twodimensional mixed convective flow past a square cylinder under the joint influence of buoyancy and free-stream orientation with respect to gravity. The numerical experiments have been conducted at a fixed Reynolds number (Re) of 100 and Prandtl number (Pr) of 0.71, while Richardson number (Ri)...

In this study, we investigated numerically heat transfer by mixed convection coupled to radiation in a square cavity; the upper horizontal wall is movable. The purpose of this study is to see the influence of the emissivity ε and the varying of the Richardson number Ri on the variation of average Nusselt number Nu. The vertical walls of the cavity are differentially heated, the left wall is mai...

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.

We describe the domino Schensted algorithm of Barbasch, Vogan, Garfinkle and van Leeuwen. We place this algorithm in the context of Haiman’s mixed and leftright insertion algorithms and extend it to colored words. It follows easily from this description that total color of a colored word maps to the sum of the spins of a pair of 2-ribbon tableaux. Various other properties of this algorithm are ...