In this paper we give convex-ear decompositions for the order complexes of several classes of posets, namely supersolvable lattices with non-zero Möbius functions and rank-selected subposets of such lattices, rank-selected geometric lattices, and rank-selected face posets of shellable complexes which do not include the top rank. These decompositions give us many new inequalities for the h-vecto...

A subalgebra $B$ of a Lie algebra $L$ is called weak c-ideal if there subideal $C$ such that $L=B+C$ and $B\cap C\leq B_{L} $ where $B_{L}$ the largest ideal contained in $B.$ This analogous to concept weakly c-normal subgroups, which has been studied by number authors. We obtain some properties c-ideals use them give characterisations solvable supersolvable algebras. also note one-dimensional ...

The class of Worpitzky-compatible subarrangements a Weyl arrangement together with an associated Eulerian polynomial was recently introduced by Ashraf, Yoshinaga and the first author, which brings characteristic Ehrhart quasi-polynomials into one formula. braid arrangement, type A, are known as graphic arrangements. We prove that arrangements characterized cocomparability graphs. This can be re...

The following paper examines properties of the weak order on the groups Sr+1 and Br+1 as motivated by the search for a combinatorial proof of known h-vector inequalities. Several general results are developed with respect to descent set domination, and an explanation of the computer programs used to generate a number of these results is presented. While this paper primarily focuses on hand flag...

Geometric lattices are characterized as those finite, atomic lattices such that every atom ordering induces a lexicographic shelling given by an edge labeling known as a minimal labeling. Equivalently, geometric lattices are shown to be exactly those finite lattices such that every ordering on the join-irreducibles induces a lexicographic shelling. This new characterization fits into a similar ...

Polar orderings arose in recent work of Salvetti and the second author on minimal CW-complexes for complexified hyperplane arrangements. We study the combinatorics of these orderings in the classical framework of oriented matroids, and reach thereby a weakening of the conditions required to actually determine such orderings. A class of arrangements for which the construction of the minimal comp...

The classical superconformal actions of branes in adS superspaces have a closed form depending on a matrix M quadratic in fermions, as found in hep-th/9805217. One can gauge-fix the local κ-symmetry using the Killing spinors of the brane in the bulk. We show that in such gauges the superconformal actions are simplified dramatically since M = 0 in all cases. The relation between classical and ga...