The key polynomials, defined by Lascoux–Schützenberger, are characters for the Demazure modules of type A. We classify multiplicity-free polynomials. proof uses two combinatorial models first is due to Kohnert. second in terms Searles’ rule quasi-key polynomials Assaf–Searles. Our argument proves a sufficient condition polynomial be multiplicity-free.

Large sets of combinatorial designs has always been a fascinating topic in design theory. These form partition the whole space into with same parameters. In particular, large set block designs, whose blocks are size k taken from an n-set, is all k-subsets n-set disjoint copies defined on and The current most intriguing question this direction whether Steiner quadruple systems exist to provide e...

Let (R,m) be a d-dimensional Noetherian local ring and E a finitely generated R-submodule of a free module R. In this work we introduce a Buchsbaum-Rim multiplicity sequence ck(E), k = 0, . . . , d + p − 1 for E that generalize the Buchsbaum-Rim multiplicity defined when E has finite colength in R as well as the Achilles-Manaresi multiplicity sequence that applies when E ⊆ R is an ideal. Our ma...

The multiplicity of a zero of a (univariate, polynomial) spline is defined in terms of its B-spline coefficients, thus making certain bounds trivial while, at the same time, adhering to the principle that the multiplicity of a zero indicates the number of simple zeros nearby achievable by a nearby element from the same class. In particular, the multiplicity depends on the class to which the fun...

A linear ball is a simplicial complex whose geometric realization is homeomorphic to a ball and whose Stanley–Reisner ring has a linear resolution. It turns out that the Stanley–Reisner ring of the sphere which is the boundary complex of a linear ball satisfies the multiplicity conjecture. A class of shellable spheres arising naturally from commutative algebra whose Stanley–Reisner rings satisf...

Process Patterns is an emergent approach and a valuable means for capitalization, reuse and management of process experiences and best practices. In the context of software engineering process, many formalisms and languages have been proposed to describe software process patterns. This multiplicity makes capitalization and/or reuse of process patterns, difficult to be achieved. This paper prese...

In this talk some of the latest data on directed sideward, elliptic, radial, and longitudinal flow at AGS energies will be reviewed. A method to identify the reaction plane event by event and the measurement of its resolution will be discussed. The distributions of global observables (transverse energy ET and charged particle multiplicity Nc), as well as those of identified particles will be sh...

We consider jet-shape observables of the type proposed recently [1, 2] where the shapes of one or more high-pT jets, produced in a multi-jet event with definite jet multiplicity, may be measured leaving other jets in the event unmeasured. We point out the structure of the full next-to–leading logarithmic resummation specifically including resummation of non-global logarithms in the leading-Nc l...

SUMMARY Emerging demands on cadastral design suggest that cadastres as a functional component of land administration are being redesigned to respond to initiatives in technology, government needs and social drivers. The movements in the property market are demonstrating the need to take into account complex commodities. The surge in regulatory requirements affecting land use and building is par...