In this paper, we consider translation and multiplication operators acting on the rings of symmetric and nonsymmetric polynomials and study their matrix coefficients with respect to the bases of Jack polynomials and interpolation polynomials. The main new insight is that the symmetric and nonsymmetric cases share a key combinatorial feature, that of a locally finite graded poset with a minimum ...

We give a new interpretation of the shifted Littlewood-Richardson coefficients $f_{\lambda\mu}^\nu$ ($\lambda,\mu,\nu$ are strict partitions). The $g_{\lambda\mu}$ which appear in decomposition Schur $Q$-function $Q_\lambda$ into sum functions $Q_\lambda = 2^{l(\lambda)}\sum_{\mu}g_{\lambda\mu}s_\mu$ can be considered as special case (here $\lambda$ is partition length $l(\lambda)$). also anoth...

rapeseed (brassica napus l.) is a crop relatively tolerant to salt. the effect of different ratios of nacl/kcl was studied in two cultivars (hyola308 and kristina) of rapeseed in 2002. canola seedlings were grown in hoagland’s solutions, which were salinized by different ratios of nacl/kcl. the treatments or kcl:nacl ratios were 0:0 (control);10:10; 20:0 (total added salt or tas=20 mol.m-3), 0:...