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 polynomials in the parameters which we call the Littlewood–Richardson polynomials. We give a combinatorial rule for their calculation by modifying an earlier resu...

We develop structural insights into the Littlewood-Richardson graph, whose number of vertices equals the Littlewood-Richardson coefficient cνλ,μ for given partitions λ, μ and ν. This graph was first introduced in [BI12], where its connectedness was proved. Our insights are useful for the design of algorithms for computing the Littlewood-Richardson coefficient: We design an algorithm for the exa...

This note is an extended abstract of my talk at the workshop on Representation Theory and Symmetric Functions, MSRI, April 14, 1997. We discuss the problem of finding an explicit description of the semigroup LRr of triples of partitions of length ≤ r such that the corresponding Littlewood-Richardson coefficient is non-zero. After discussing the history of the problem and previously known result...

Gutierrez, E., Seebacher, N., Arzuman, L., Kovacevic, Z., Lane, D., Richardson, V., Merlot, A., Lok, H., Kalinowski, D., Sahni, S., Jansson, P., Richardson, D. (2016). Lysosomal membrane stability plays a major role in the cytotoxic activity of the antiproliferative agent, di-2-pyridylketone 4,4-dimethyl-3thiosemicarbazone (Dp44mT). Biochimica et Biophysica Acta: international journal of bioche...

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 analogous to the famed version of the classical Littlewood-Richardson rule involving Yamanouchi words. Furthermore, both our rules contain this classical Littlewood...

mixed convection is a fundamentally significant heat transfer mechanism that occurs in selection industrial and technological applications. in this study, first the laminar mixed convection inside rectangular enclosure with moving wall and aspect ratio=10 is modeled and then the results are compared with other investigate. after showing varity of results, the investigation is continued with tur...

The surface stress is computed by the method of geostrophic departures using 23 days of double theodolite wind observations at Shilo, Manitoba. The main results are as follows. Relations between the stress and the geostrophic wind fit these data better than do similar expressions using the surface wind. The stress varies linearly, rather than quadratically, with wind speed. For a given surface ...

This paper focuses on the GLn tensor product algebra, which encapsulates the decomposition of tensor products of arbitrary irreducible representations of GLn. We will describe an explicit basis for this algebra. This construction relates directly with the combinatorial description of Littlewood-Richardson coefficients in terms of Littlewood-Richardson tableaux. Philosophically, one may view thi...

Advection equations appear often in large-scale mathematical models arising in many fields of science and engineering. The Crank-Nicolson scheme can successfully be used in the numerical treatment of such equations. The accuracy of the numerical solution can sometimes be increased substantially by applying the Richardson Extrapolation. Two theorems related to the accuracy of the calculations wi...