منابع مشابه
Shelling the coset poset
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...
متن کاملThe Coset Poset and Probabilistic Zeta Function of a Finite Group
For a finite group G and a non-negative integer s, let P(G,s) be the probability that a randomly chosen s-tuple generates G. Philip Hall gave an explicit formula for P(G,s), exhibiting the latter as a finite Dirichlet series. One can therefore speak of P(G,s) for an arbitrary complex number s. The reciprocal of this function of s is called the zeta function of G. The present work arose from an ...
متن کاملAveraged shelling for quasicrystals
The shelling of crystals is concerned with counting the number of atoms on spherical shells of a given radius and a fixed centre. Its straight-forward generalization to quasicrystals, the so-called central shelling, leads to non-universal answers. As one way to cope with this situation, we consider shelling averages over all quasicrystal points. We express the averaged shelling numbers in terms...
متن کاملA Note on Shelling
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 ...
متن کاملOn the shelling antimatroids of split graphs
Chordal graph shelling antimatroids have received little attention with regard to their combinatorial properties and related optimization problems, as compared to the case of poset shelling antimatroids. Here we consider a special case of these antimatroids, namely the split graph shelling antimatroids. We show that the feasible sets of such an antimatroid relate to some poset shelling antimatr...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2007
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2006.08.010