Abstract We determine the metric dimension of annihilating-ideal graph a local finite commutative principal ring and with two maximal ideals. also find bounds for an arbitrary ring.

A graph G = (V, E) is called a split graph if there exists a partition V = I∪K such that the subgraphs G[I] andG[K] of G induced by I andK are empty and complete graphs, respectively. In 1980, Burkard and Hammer gave a necessary condition for a split graph G with |I| < |K| to be hamiltonian. We will call a split graph G with |I| < |K| satisfying this condition a Burkard–Hammer graph. Further, a...

The lattice of noncrossing set partitions is known to admit an R-labeling. Under this labeling, maximal chains give rise to permutations. We discuss structural and enumerative properties of the lattice of noncrossing partitions, which pertain to a new permutation statistic, m(a), defined as the number of maximal chains labeled by 0. Miibius inversion results and related facts about the lattice ...

We give several examples of designs and antidesigns in classical finite polar spaces. These types of subsets of maximal totally isotropic subspaces generalize the dualization of the concepts of m-ovoids and tight sets of points in generalized quadrangles. We also consider regularity of partial spreads and spreads. The techniques that we apply were developed by Delsarte. In some polar spaces of ...

Suppose a strict preference relation fails to possess maximal elements, so that a choice is not clearly defined. I propose to delete particular instances of strict preferences until the resulting relation satisfies one of a number of known regularity properties (transitivity, acyclicity, or negative transitivity), and to unify the choices generated by different orders of deletion. Removal of st...

This article investigates the manipulation of polygonal parts using a simple device consisting of a grid of retractable pins mounted on a vertical plate. This “Pachinko machine” is intended as a reconfigurable parts feeder for flexible assembly. A part dropped on this device may come to rest on the actuated pins, bounce out, or fall through. The authors propose a novel algorithm for part reorie...

It is known [l; 2] that every inverse semigroup 5 has a faithful representation as a semigroup of (1, l)-mappings of subsets of a set A into A. The set A may be taken as the set of elements of 5 and the (1, l)-mappings as mappings of principal left ideals of 5 onto principal left ideals of 5. If £ is the set of idempotents of 5 then there is also a representation of 5, not necessarily faithful,...