The analysis of the Tutte polynomial of a matroid using activities is associated with a shelling of the family of spanning sets. We introduce an activities analysis of the reliability of a system specified by an arbitrary clutter, associated with an S-partition rather than a shelling. These activities are related to a method of constructing Boolean interval partitions developed by Dawson in the...

A homogeneous medium is characterised by a point set in Euclidean space (for the atomic positions, say), together with some self-averaging property. Crystals and quasicrystals are homogeneous, but also many structures with disorder still are. The corresponding shelling is concerned with the number of points on shells around an arbitrary, but fixed centre. For non-periodic point sets, where the ...

Corresponding Author: Hui Huang Agricultural Product Processing Research Institute at Chinese Academy of Tropical Agricultural Sciences, Chinese Agricultural Ministry Key Laboratory of Tropical Crop Products Processing, Zhanjiang524001, China Email: [email protected] Abstract: The aim of this study is to determine the optimal parameters of the adaptive cashew shelling cutter. To meet the requ...

Best nitrogen management practices are the pre-requisite to warrant high maize yield. Thus, experiments were conducted to study the “effect of tillage and split application of nitrogen on hybrid maize” under semi-arid conditions of Pakistan, during fall 2008 and 2009. The experiments were laid out in randomized complete block design with split-plot arrangement, replicated three times in a net p...

The radial distribution function is a characteristic geometric quantity of a point set in Euclidean space that reflects itself in the corresponding diffraction spectrum and related objects of physical interest. The underlying combinatorial and algebraic structure is well understood for crystals, but less so for non-periodic arrangements such as mathematical quasicrystals or model sets. In this ...

It is shown that the coset lattice of a finite group has shellable order complex if and only if the group is complemented. Furthermore, the coset lattice is shown to have a Cohen–Macaulay order complex in exactly the same conditions. The group theoretical tools used are relatively elementary, and avoid the classification of finite simple groups and of minimal finite simple groups. © 2006 Elsevi...

A polytopal digraph G(P ) is an orientation of the skeleton of a convex polytope P . The possible non-degenerate pivot operations of the simplex method in solving a linear program over P can be represented as a special polytopal digraph known as an LP digraph. Presently there is no general characterization of which polytopal digraphs are LP digraphs, although four necessary properties are known...

We prove that the external activity complex Act<(M) of a matroid is shellable. In fact, we show that every linear extension of LasVergnas’s external/internal order <ext/int on M provides a shelling of Act<(M). We also show that every linear extension of LasVergnas’s internal order <int on M provides a shelling of the independence complex IN(M). As a corollary, Act<(M) and M have the same hvecto...