In this paper we extend some aspects of the theory of 'supersolvable lattices' [3] to a more general class of finite lattices which includes the upper-semimodular lattices. In particular, all conjectures made in [33 concerning upper-semimodular lattices will be proved. For instance, we will prove that if L is finite upper-semimodular and if L' denotes L with any set of 'levels' removed, then th...

We show that any congruence lower semimodular variety whose 2-generatecl free algebra is finite must be congruence modular.

This paper presents a general inequality for the grating lobes of the planar phased array, whether rectangular lattice or triangular lattice. And for the planar phased array with grating lobes, the maximum scanning angle is given.

For subnormal subgroups A / B and C / D of a given group G, the factor B/A will be called subnormally down-and-up projective to D/C, if there are subnormal subgroups X /Y such that AY = B, A∩Y = X , CY = D and C∩Y = X . Clearly, B/A ∼= D/C in this case. As G. Grätzer and J.B. Nation [6] have just pointed out, the standard proof of the classical Jordan-Hölder theorem yields somewhat more than wi...

All lattices are assumed to be finite. Björner [2] has shown that a dismantlable (see Rival, [5]) lattice L is Cohen-Macaulay (see [6] for definition) if and only if L is ranked and interval-connected. A lattice is planar if its Hasse diagram can be drawn in the plane with no edges crossing. Baker, Fishburn and Roberts have shown that planar lattices are dismantlable, see [1]. Lexicographically...

7 An antimatroid is a family of sets such that it contains an empty set, and it is accessible and closed under union of sets. An antimatroid is an ‘antipodal’ concept of matroid. 9 We shall show that an antimatroid is derived from shelling of a poset if and only if it does not contain a minor isomorphic to S7 where S7 is the smallest semimodular lattice that is not 11 modular. It is also shown ...

We show that the left/right relation on the set of s-t-paths of a plane graph induces a so-called submodular lattice. If the embedding of the graph is s-t-planar, this lattice is even consecutive. This implies that Ford and Fulkerson’s uppermost path algorithm for maximum flow in such graphs is indeed a special case of a two-phase greedy algorithm on lattice polyhedra. We also show that the pro...